area and perimeter problem solving tes

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Area and Perimeter

This SMILE resource contains three packs of games, investigations, worksheets and practical activities supporting the teaching and learning of area and perimeter, from calculating area by counting squares to finding the formula for the area of a trapezium.

Area and Perimeter pack one  contains fourteen work cards with a wide variety of activities covering finding areas by counting squares, finding the length of perimeters by counting, developing the formula for the area of a rectangle, drawing different shapes with a given perimeter, finding different shapes with a given area and finding the area of simple compound shapes.

Area and Perimeter pack two  contains eleven work cards with activities requiring students to make shapes of a given size using pentominoes, investigate the area and perimeter of rectangles, find the area of a right-angled triangle, calculate the area of polygons drawn on square dotted paper, investigate different ways of shading half a square, find the area of a triangle, find the area of compound shapes made from rectangles and find the area of a parallelogram.

Area and Perimeter pack three  contains eleven work cards with activities in which students investigate the connections between the area of a parallelogram and the area of a rectangle, the area of obtuse-angled triangles, further parallelogram problems, finding the area of a polygon, finding the area of a trapezium and calculating the area of irregular shapes.

SMILE (Secondary Mathematics Individualised Learning Experiment) was initially developed as a series of practical activities for secondary school students by practising teachers in the 1970s. It became a complete individualised scheme based around a network of activity cards and assessments. Related resources include answers  to all of the cards and test books and answers .

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Problem solving with perimeter and area

You can use your knowledge of perimeter and area to solve problems.

Lesson details

Key learning points.

• Problems in context involving perimeter can be solved.
• Problems in context involving area can be solved.
• The units of measurement should be the same.

Common misconception

Pupils may struggle to determine whether a question is asking about the perimeter or the area.

Encourage pupils to draw a diagram to represent the situation as this can make it clearer as to whether perimeter or area is required.

Area - The area is the size of the surface and states the number of unit squares needed to completely cover that surface.

Perimeter - The perimeter is the distance around a 2D shape.

This content is © Oak National Academy Limited ( 2024 ), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Perimeter, Area and Volume Short Problems

This is part of our collection of Short Problems . You may also be interested in our longer problems on Perimeter, Area and Volume Age 11-14 and Age 14-16 . Printable worksheets containing selections of these problems are available here:

Six Circles

Squares in a Square

Chequered Cuboid

Star in a Hexagon

Cuboid faces

Giant Rubik's Cube

Nested Squares

Mid-point area.

Cubes on a Cube

Line of Squares

Strawberries and Peas

Leaning Over

Christmas Cut-Out

Hawaiian earring.

Scalene area

Tile border

Tilted tank

Double Cover

Dividing a square

Exactly Three-Quarters

Semicircle shape.

Packing small boxes

Tangram Area

Triangles' triangle.

Intersecting Squares

Sideways Ratio

Cubic Masterpiece

Open the Box

rectangle split

Hexagon Slices

Triangle in a hexagon.

Four Square

Pile Driver

Annulus Area

Bobbly perimeter

Semicircle Stack

Ratio of areas.

Crazy Shading

Penny Farthing

Semicircular Design

Square in a circle in a square

Circle in a Semicircle

Half an annulus.

Pencil Turning

Maximised Area

Cones and spheres

Canny Fraction

Sticky Tape

Loo roll emergency

Candy floss, similar cylinders.

Square Ratio

Rolling Inside

Rectangle Cutting

Circled Corners

Wood Pile Perimeter

Four Leaf Clover

Emptied Cube

Square Flower

Trisected Triangle

Semicircle distance

Sinking Feeling

Running Race

Tilted Aquarium

Cut-Up Square

Mr Barton Maths Podcast

Long-form conversations about teaching and learning with craig barton, tes top 10 resources: perimeter, area and volume.

The following collection of resources have been assembled by the TES Maths Panel . They can be downloaded for free by registering on the TES website.

Perimeter, area and volume can be a fairly tedious topic to teach. On the other hand, it has the potential to be brought to life to capture students’ imagination and interest. Remembering formulae isn’t the way for students to learn this topic; it is through visual and interactive learning that it will stick.

Top 10 resources:

1. Circumference and perimeter treasure hunt

Age range:  11 – 16  Format:  PDF

An easy to use resource to challenge pupils. The compound shape questions are particularly useful.

2. Drawing, volume and surface area of prisms

Age range:  11 – 16  Format:  Word document

A functional resource that develops a variety of skills and comes with a plentiful list of extension tasks.

3. Area puzzle starter

An unusual resource to get students thinking at the start of a lesson.

4. Volume of revolution

Age range:  16 – 18  Format:  PDF

Learn how to use Autograph to teach volumes of revolution – an effective way to aid students’ understanding of 3D problems.

5. Area and perimeter of triangles

An engaging resource that requires students to find the area and perimeter of triangles – includes an extension task to consolidate understanding.

6. Finding the volume and surface area of a cuboid

Age range:  11 – 16  Format:  .swf

This resource provides help to students struggling to visualise cuboid related problems.

7. Pyramid volume proof

Age Range:  11 – 16  Format:  Web

A practical lesson that results in students deriving the formula for the volume of a pyramid.

8. Area and perimeter follow-me cards

This plenary activity offers a wide range of questions on a variety of shapes to challenge students’ understanding.

9. GCSE maths: Evaluating statements – length and area

Age range: 11 – 16  Format:  PDF

Challenge pupils and aid deeper understanding of conjectures with this series of statements and investigation task.

10. Area and perimeter PowerPoint 

Age range:  11 – 16  Format:  PowerPoint presentation

Visual and contextual ideas for creating or adapting a lesson on area and perimeter.

Colm Lynch,  maths secondary panel

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Key Stage 3 - Geometry

Standard KS3.G.1.1 - Calculate the area and perimeter of rectangles and squares with word problems.

Included Skills:

Geometry and measures • Pupils should be taught to: - derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders) - calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes - draw and measure line segments and angles in geometric figures, including interpreting scale drawings - derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line - describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric - use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles - derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies - identify properties of, and describe the results of, translations, rotations and reflections applied to given figures - identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids - apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles - understand and use the relationship between parallel lines and alternate and corresponding angles - derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons - apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras' Theorem, and use known results to obtain simple proofs - use Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles - use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D - interpret mathematical relationships both algebraically and geometrically.

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Breadcrumbs

• Area / perimeter of rectangles

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Area and perimeter of rectangles

Geometry worksheets: finding the area and perimeter of rectangles.

Students are given the measurements of two sides of each rectangle in customary units (inches, feet, yard) and calculate the area and perimeter in the appropriate measurement units .

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Browse all of our geometry worksheets , from the basic shapes through areas and perimeters, angles, grids and 3D shapes.

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Year levels.

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Expected level of development

Australian Curriculum Mathematics V9 :  AC9M5M02

Numeracy Progression : Understanding units of measurement: P7

At this level, students estimate and measure perimeter in metric units for length and area of quadrilaterals using grid squares and square centimetres. They solve practical problems involving the perimeter and area of regular and irregular shapes.

Use explicit teaching and questioning to help students differentiate between the concepts of area and perimeter.

Provide students with activities to develop an understanding of the fact that area and perimeter are not dependent on each other (for example, a shape with a perimeter of 12 cm may have multiple different areas, depending on the shape and its dimensions).

When measuring the area of familiar shapes such as a rectangle, students will use square centimetres or grid paper to cover regions, and they may discover familiar representations (such as rows and columns that resemble arrays used in multiplication). They add the rows to calculate the area. Note that in Year 6, students are expected to use the area formula for area of rectangles: A = L × W.

Make explicit efficient ways to calculate the perimeters of rectangles. Look for alternate ways to calculate perimeter P = L + L + W + W and P = 2L + 2W, which shows that both the length and width are doubled then added together. An alternative version of this rule is P = 2(L + W), where students first add the length and width then multiply the result by two (double).

Teaching and learning summary:

• Use explicit teaching and questioning when discussing concepts of area and perimeter.
• Enable students to discover efficient ways to calculate the perimeters of rectangles.
• Investigate situations that involving perimeter.
• Present area problems that require students to reason, use space efficiently, fit a set number of objects.

• describe how to calculate perimeter and area of a quadrilateral
• compare and order 2D shapes according to their area
• use metric units to measure perimeter and area.

Some students may:

• confuse the formulas for finding area and perimeter. Rather than providing students with the formula, A = L × W, provide opportunities for them to discover this themselves. This is primarily because the formulas are introduced too early and before students have developed a conceptual understanding of area and perimeter. It is important to use concrete, pictorial and abstract representations when teaching these concepts.
• have trouble understanding that if a shape is cut up and re-formed it will still have the same area (conservation of area). Revisiting properties of 2D shapes may help develop this understanding.
• believe that there is a direct relationship between area and perimeter. They may believe that surfaces with the same area must have the same perimeter, and vice versa. Challenge this thinking through a variety of activities to demonstrate the lack of relationship between the one-dimensional perimeter and the two-dimensional area.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning how to measure area using formal units.
• We are learning how to decompose and rearrange shapes to find their areas.

Why are we learning about this?

• Area helps you to quantify physical space. In real life, area measurements can help with working out quantities, for example, how much wallpaper is needed to cover a wall.
• Find a large box. Estimate how much wrapping paper you would need to wrap the box. Record your estimation.
• Cover one face of the box with a sheet of wrapping paper. Mark the around edges of the box on the non-coloured side of the wrapping paper. Work out the area of that face. Record your answer.
• Repeat the steps above for the remaining five faces of the box.
• Calculate the total area of the wrapping paper needed to cover the box. 
• Draw a diagram to show all your measurements.

Success criteria

• find the area of a rectangular shape
• combine areas of a shape when working out the area of a box
• estimate and work out how much wrapping paper is required to cover a box.

Please note:  This site contains links to websites not controlled by the Australian Government or ESA. More information  here .

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Teaching strategies.

A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well. 

Explicit teaching

Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.

Questioning

A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.

Mathematics investigation

By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.

Culturally responsive pedagogies

Culturally responsive pedagogy is a form of teaching that incorporates learners’ cultural background and histories into classroom practice.

Teaching resources

A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.

Farm fence fractions

In this lesson, we explore fractions, decimals and perimeter.

reSolve: Area and perimeter

Students consolidate their understanding of and skills in calculating the area and the perimeter of rectangles.

4 by 3 rectangle inquiry

Students investigate rectangles with an area of 12 square units and, through problem-solving, look for relationships between area and perimeter.

Numerically equal

This problem requires students to consider area and perimeter at the same time, and to know the difference between the two.

Patrolling the perimeter

Students measure the dimensions of rectangles (including squares) in the environment, then estimate and measure their perimeters.

An absorbing challenge

Students estimate the area of irregular shapes and then check the accuracy of their effort.

Area builder

Use this interactive tool to explore the relationship between area and perimeter.

Wallpaper Area

This task is designed to help students understand the meaning of area. It challenges students to arrange pieces of wallpaper in order of size and explain their decisions.

How many rectangles?

Use this video to explore area and perimeter.

Area and perimeter: Video and teaching guide

Use this video to explore concepts of area and perimeter, and connect these ideas to real-world situations.

Finding the areas of rectangles using side lengths

Students find areas of rectangles by measuring and multiplying side lengths.

Area and scaling

Use this set of teacher slides to extend and apply students’ thinking about area.

Relevant assessment tasks and advice related to this topic.

By the end of Year 5, students are choosing and using appropriate metric units to measure the attributes of length, mass and capacity, and to solve problems involving perimeter and area.

Lengths and areas

Use the student resources to enable students to self-check answers to length, area and perimeter problems.

Mathematics: ACARA work sample portfolio summary – Year 5

Refer to Work sample 7, 'Measurement – Using perimeter and area' and the related task for guidance in assessing students’ understanding of perimeter and area.

What is the area?

Use this diagnostic task to assess what students know about area and using the area formula.

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Same Perimeter, Different Area Word Problems – Worksheet

Updated:  27 Oct 2023

Practice solving multi-step word problems involving objects that have the same perimeter but different areas.

Editable:  Google Slides

Non-Editable:  PDF

Pages:  4 Pages

• Curriculum Curriculum:  CCSS, TEKS

Grades:  3 - 4

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Same Perimeter, Different Area Word Problems

Have your students mastered the basic concepts of perimeter and area ? If so, they may be ready for more challenging math problems where they have to use multiple operations to solve a problem. These multi-step word problems will give your students an opportunity to answer questions where they have to use the perimeter of one object, determine the missing side length of another object, and then calculate the area.

With this worksheet, students will have the opportunity to practice solving 8 problems where 2 objects have the same perimeter but different areas. Questions may include those such as: 

James’ sandbox is 8 feet long by 4 feet wide. Tommy’s sandbox has a length of 6 feet. If James and Tommy both have sandboxes with the same perimeter, what are the areas of the two sandboxes? 

Samantha and Carly have playrooms of the same perimeter but different areas. Carly’s playroom is 8 feet long by 7 feet wide. One of the walls in Samantha’s playroom is 5 feet long. Who has the playroom with the larger area?

An answer key is included with your download to make grading fast and easy!  

Tips for Differentiation + Scaffolding 

In addition to independent student work time, use this worksheet as an activity for:

• Guided math groups  
• Lesson wrap-up
• Fast finishers  
• Homework assignment
• Whole-class review (via smartboard)

For students who need a bit of a challenge, consider assigning one of the additional versions of this resource:

Perimeter Word Problems – Mixed Problem Types

Unknown Side Perimeter Word Problems

If there are students who need support, consider completing this worksheet in a 1-on-1 setting or in a small group setting. Additionally, work with students to draw a picture to solve each problem. There also is a version of this resource where students practice solving standard perimeter problems .

🖨️ Easily Download & Print

Use the dropdown icon on the Download button to choose between the PDF or editable Google Slides version of this resource. 

Because this resource includes an answer sheet, we recommend you print one copy of the entire file. Then, make photocopies of the blank worksheet for students to complete. 

To save paper, we suggest printing this 2-page worksheet double-sided.

Turn this teaching resource into a sustainable activity by printing on cardstock and slipping it into a dry-erase sleeve. Students can record their answers with a whiteboard marker, then erase and reuse them. 

Additionally, project the worksheet onto a screen and work through it as a class by having students record their answers in their notebooks. 

Get more worksheets to have handy!

This resource was created by Nicole Ellis, a teacher in New York and Teach Starter Collaborator. 

Don’t stop there! We’ve got more activities to shorten your lesson planning time:  

teaching resource

Perimeter worksheet.

Use these perimeter worksheets in your math lessons when teaching your students how to apply various formulae to calculate the perimeter of shapes.

Find the Missing Side Worksheet

Use this missing side perimeter worksheet to help your students find the missing sides on a collection of rectangles and squares.

Number Talks - Perimeter and Area Task Cards

Build number sense skills with this set of 28 task cards.

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Perimeter and Area (Problem Solving)

Subject: Maths for early years

Age range: 3-5

Resource type: Assessment and revision

Last updated

20 January 2015

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This could have been a good resource, however the English is really poor and not something I want to be modelling to my students. It's a shame really.

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