perimeter problem solving ks3

Perimeter, Area, Volume

Part of Maths

Learn about perimeters and how to calculate the perimeter of a simple shape with this BBC Bitesize Maths article. For students between the ages of 11 and 14.

Area of squares, rectangles and compound shapes

Learn about the area of squares, rectangles and compound shapes with this BBC Bitesize Maths article. For students between the ages of 11 and 14.

Area of triangles

Learn how to calculate the area of triangles with this BBC Bitesize Maths article. For students between the ages of 11 and 14.

Area of parallelograms

Learn about the area of parallelograms with this BBC Bitesize Maths article. For students between the ages of 11 and 14.

Area of trapeziums

Learn about area of trapeziums with this BBC Bitesize Maths article. For students between the ages of 11 and 14.

What is pi? - Circumference of a circle

Learn about definition of pi in relation to a circle.

Area of circles

Learn about the area of circles with this BBC Bitesize Maths article. For students between the ages of 11 and 14.

Surface area of cubes and cuboids

Learn about the surface area of cubes and cuboids with this BBC Bitesize Maths article. For students between the ages of 11 and 14.

Volume of cubes and cuboids

Learn how to find the volume of cubes and cuboids with this BBC Bitesize Maths article. For students between the ages of 11 and 14.

Surface area and volume of a cylinder

Learn about the surface area and volume of a cylinder with this BBC Bitesize Maths article. For students between the ages of 11 and 14.

Surface area and volume of prisms

Learn about the surface area and volume of prisms with this BBC Bitesize Maths article. For students between the ages of 11 and 14.

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The perimeter of a shape is the sum of its side lengths. It is important to label all side lengths so you don't miss any out.

• To find the perimeter of this shape, we need to add all the side lengths together.

Example 1 cont.

• To find the perimeter of this shape, we need to add all the side lengths.

Example 2 cont.

Missing length

• Sometimes you might need to work out the missing length of a shape in order to find the perimeter.
• What is the perimeter of the rectangle above?

• We use the information that rectangles have two pairs of sides of equal length to work out the length of the missing side.

1.1 Place Value

1.1.1 Ordering Numbers

1.1.2 Comparing Numbers

1.1.3 Equals Symbols

1.1.4 Adding Negative Numbers

1.1.5 Subtracting Negative Numbers

1.1.6 Multiplying Negative Numbers

1.1.7 Dividing Negative Numbers

1.1.8 End of Topic Test - Place Value

1.2 Factors & Multiples

1.2.1 Factors

1.2.2 Prime Numbers

1.2.3 Multiples

1.2.4 Prime Factors

1.2.5 Highest Common Factors

1.2.6 Highest Common Factor Prime Factors

1.2.7 Lowest Common Multiples

1.2.8 Lowest Common Multiples Prime Factors

1.2.9 End of Topic Test - Factors & Multiples

1.3 Operations

1.3.1 Addition

1.3.2 Subtraction

1.3.3 Multiplication 10,100...

1.3.4 Grid Multiplication

1.3.5 Division by 10s

1.3.6 Powers

1.3.7 Roots

1.3.8 Surds

1.3.9 Rationalise denominator

1.3.10 Simplify Surds

1.3.11 BIDMAS

1.3.12 Inverse Ops

1.3.13 Standard Form

1.3.14 Addition in Standard Form

1.3.15 Subtraction in Standard Form

1.3.16 End of Topic Test - Standard Form

1.4 Fractions, Decimals & Percentages

1.4.1 Fractions

1.4.2 Mixed & Improper Fractions

1.4.3 Write 2 Numbers as Fractions

1.4.4 Adding Fractions

1.4.5 Subtracting Fractions

1.4.6 Multiplying Fractions

1.4.7 Dividing Fractions

1.4.8 Finding Fractions

1.4.9 Improper & Mixed Fractions

1.4.10 Decimal Place Value

1.4.11 Fraction to Decimal

1.4.12 Find Percentage Unitary

1.4.13 Fraction to Percentage

1.4.14 Percentage to Fraction

1.4.15 Percentage to Decimal

1.4.16 Decimal to Percentage

1.4.17 Percentage using Decimal

1.4.18 End of Topic Test - Fractions

1.5 Growth & Decay

1.5.1 Population Growth

1.5.2 Compound Growth & Decay

1.5.3 Compound Interest

1.5.4 Compund Interest 2

1.5.5 Depreciation

1.6 Measurements & Units

1.6.1 Standard Units 1

1.6.2 Standard Units 2

1.6.3 Standard Units 3

1.6.4 Length

1.6.6 Volume

1.6.7 Capacity

1.6.9 Money

1.6.10 Mass

1.7 Accuracy

1.7.1 Decimal Rounding

1.7.2 SigFig Rounding

1.7.3 Estimations

1.7.4 Upper Lower Bounds

2.1 Introduction to Algebra

2.1.1 Algebra Basics

2.1.2 Algebraic Concepts

2.1.3 Writing Expressions

2.1.4 Collecting Terms

2.1.5 Common Factors

2.1.6 Expanding Brackets

2.1.8 Rearranging Formulae

2.1.9 End of Topic Test - Introduction to Algebra

2.2.1 Coordinates

2.2.2 Gradient and Intercept

2.2.3 Calculate Gradient &Y-intercept

2.2.4 Finding Equation

2.2.5 Quadratic Graphs

2.3 Solving Equations

2.3.1 Solve Linear Equations

2.3.2 Words To Equation

2.3.3 Solve Linear Equations Graphically

2.3.4 Solve Inequality

2.3.5 Graphing Inequalities

2.3.6 End of Topic Test - Graphs & Equations

2.3.7 Simultaneous Equations

2.3.8 Simultaneous Equations Graph

2.3.9 Quadratic +/-

2.3.10 Factorise Quadratics

2.3.11 Complete the Square

2.4 Sequences

2.4.1 Arith & Geo Sequences

2.4.2 Key Sequences

2.4.3 Nth Term Rules

2.4.4 Find NthTerm in Linear Sequence

2.4.5 End of Topic Test - Sequences

2.4.6 Find Nth Term in Quadratic Sequence

3 Ratio, Proportion & Rates of Change

3.1 Manipulating Ratios

3.1.1 Manipulating Ratios

3.1.2 Turn Ratios into Equations

3.1.3 Part:Part Ratio

3.1.4 Part:Whole Ratio

3.1.5 Differences in Ratios

3.1.6 Fractions in Ratios

3.1.7 Ratios to Fractions

3.2 Ratios in Practice

3.2.1 Covert Units

3.2.2 Formula Triangles

3.2.3 Scale Factors

3.2.4 End of Topic Test - Ratios

3.2.5 Ratios in Shapes

3.3 Percentage & Finance

3.3.1 Percentage Increase/Decrease

3.3.2 Percentage Change

3.3.3 Original Value

3.3.4 Profit, Interest & Discount

3.3.5 Simple Interest

3.4 Proportion

3.4.1 Proportion

3.4.2 Direct Proportion

3.4.3 Inverse Proportion

3.4.4 End of Topic Test - Percentages & Proportion

4 Geometry & Measures

4.1 Introduction to Geometry

4.1.1 LinesAngles1

4.1.2 LinesAngles2

4.1.3 Regular Polygons

4.1.4 Triangles and Angles

4.1.5 Quadrilaterals

4.1.6 Midpoints

4.1.7 Bisectors and Perpendiculars

4.1.8 Angle Rules

4.1.9 Angles in Parallel Lines

4.1.10 Angles in a Polygon

4.1.11 Angles in a Triangle

4.1.12 Bearings

4.1.13 End of Topic Test - Geometry

4.2 Ruler & Compass Constructions

4.2.1 Midpoint

4.2.2 Bisectors and Perpendiculars

4.3 Perimeter & Area

4.3.1 Perimeter

4.4 Triangles, Quadrilaterals & Circles

4.4.1 Types of Triangle

4.4.2 Angles & Triangles

4.4.3 Congruence

4.4.4 Congruent Triangles

4.4.5 Similar Triangles

4.4.6 Scale Factors & Enlargement

4.4.7 Properties of Circle 1

4.4.8 Properties of a Circle 2

4.4.9 Area of a Circle

4.4.10 Circumference of a Circle

4.5 Transformations

4.5.1 Types of Transformations

4.5.2 Effects of Transformations

4.6 Triangle Formulae

4.6.1 Pythagoras' Theorem

4.6.2 Trigonometric Ratios

4.7 3D Shapes

4.7.1 Types of 3D Shape

4.7.2 Plans & Elevations

4.7.4 Volume of 3D Shapes

4.7.5 Volume of a Cuboid

4.7.6 Volume of a Cylinder

4.7.7 Volume of a Sphere

4.7.8 Volume of a Hemisphere

4.7.9 Volume of a Cone

4.7.10 Volume of a Pyramid

4.7.11 Surface Area of a Cuboid

4.7.12 Surface Area of a Cylinder

4.7.13 Surface Area of a Sphere/Hemisphere

4.7.14 Surface Area of a Cone

4.7.15 Surface Area of Composite Shapes

4.7.16 End of Topic Test - Triangles, Area, & 3D Shapes

4.8 Vectors

4.8.1 Vector Introduction

4.8.2 Vectors

5 Probability

5.1 Introduction to Probability

5.1.1 Probability

5.1.2 Probability scale

5.1.3 Randomness & Fairness

5.1.4 Sum of Probabilities

5.1.5 Relative & Expected Frequency

5.1.6 Frequency Tables

5.1.7 Use Frequency Trees

5.1.8 Complete Frequency Trees

5.2 Representing Probability

5.2.1 Sample Space Diagrams

5.2.3 Venn Diagrams

5.3 Probability Calculations

5.3.1 Theoretical Probability

5.3.2 Venn Diagram Probabilities

5.3.3 Multiple Events

5.3.4 Dependent & Independent Events

5.3.5 Calculating Probabilities

5.3.6 Complex Tree Diagrams

5.3.7 End of Topic Test - Probability

6 Statistics

6.1 Introduction to Statistics

6.1.1 Statistics Basics

6.1.2 Statistics Basics 2

6.1.3 Comparing Data

6.1.4 Comparing Datasets

6.1.5 Writing Comparisons

6.1.6 Frequency Table

6.2 Charts & Graphs

6.2.1 Bar Charts

6.2.2 Pie Charts

6.2.3 Pictograms

6.2.4 Scatter Graphs

6.2.5 Making Predictions

6.2.6 Correlation and Causation

6.2.7 Outliers

6.2.8 End of Topic Test - Statistics

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KS3: Area and Perimeter of a Rectangle

Subject: Mathematics

Age range: 11-14

Resource type: Lesson (complete)

Last updated

7 September 2018

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KS3 Area and Perimeter Worksheets

Maths Worksheets / KS3 Area and Perimeter Worksheets

Area of Non-Right Angled Triangles

Area of Quadrilaterals (A)

Area of Right Angled Triangles

Compound Shapes (A)

Tiling Problems (A)

Area and Circumference

Area of 2D shapes

Area of Circles

Area of Quadrilaterals (B)

Area of Trapezia (A)

Area of Trapezia (B)

Circle Area Problems

Circumference

Compound Shapes (B)

Solving Equations Involving Area of Rectangles

Area of Sectors and Arc Lengths

Finding the Radius or Diameter

Surface Area of Cones and Spheres

Surface Area of Prisms

The Formulae for Area of Sectors and Arc Lengths

Area of Sectors and Segments

Area of Sectors and Segments (With Clues)

Area of Triangles (With Clues)

Printable Area and Perimeter Worksheets With Answers

Why is learning about area and perimeter important.

Calculating perimeters and areas is an important skill which is used by many people in their everyday lives.

Architects, engineers and construction workers will need precise measurements of area and perimeter in order to construct a building to the right specification. It is not just professionals that need a solid knowledge of area and perimeter; knowing the area of a room can help work out how much paint or flooring is needed to fill the space when redecorating.

Improve Students’ Problem Solving Skills

Regularly practicing area and perimeter questions with children can help them develop good problem solving and logic skills.

The importance of these skills should not be underestimated, as these skills are useful for their learning in other subjects, as well as preparing them for the workplace.

Worksheets Make Learning Area and Perimeter Enjoyable

Children start learning about perimeters and areas in KS2, so it is important to use area and perimeter materials which make the topic easy to understand and enjoyable for them.

Worksheets with fun activities help children learn about this important area of maths. Using good quality resources throughout their education will prepare children for more advanced area and perimeter questions, such as calculating areas of compound shapes and areas of sectors.

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Area and Perimeter

The area of a shape is the space inside the shape. Area is measured in squares.

Finding the area of a rectangle

Here is a rectangle drawn on a centimetre grid.

To find the area of a rectangle multiply the length by the width. (We could also count the squares but this will not work from more complex questions)

In this example we have a length of 6cm and a width of 3cm.

Area = length × width Area = 6 × 3 Area = 18 cm 2

The units are cm 2 : one cm 2 is a square that measures 1cm by 1 cm.

Example 1: A rectangle is drawn on a centimetre grid Calculate the area of the rectangle

Area = length × width Area = 5 × 4 Area = 20cm 2

A rectangle is drawn on a centimetre grid. Calculate the area of the rectangle.

Finding the area of a triangle

We can think of a triangle as half of a rectangle

To calculate the area of a triangle we can half the area of a triangle

The area of a triangle = 1 ⁄ 2 × base × height

Example 2: Here is a triangle drawn on a centimetre grid. Calculate the area of the triangle.

Area = 1 ⁄ 2 × base × height Area = 1 ⁄ 2 × 4 × 6 Area = 2 × 6 Area = 12cm 2

Example 3: Calculate the area of the triangle.

For the area calculation we use the perpendicular height (it must be straight up, not diagonal). The height of this triangle is 12 metres.

Area = 1 ⁄ 2 × base × height Area = 1 ⁄ 2 × 8 × 12 Area = 4 × 12 Area = 48m 2

A triangle is drawn on a centimetre grid. Calculate the area of the triangle.

Calculate the area of the triangle.

Finding the area of a parallelogram

A parallelogram is a quadrilateral with two sets of parallel sides.

A parallelogram can be made into a rectangle by cutting off and moving a triangle:

The area of a parallelogram = base × height

Example 4: Here is a parallelogram drawn on a centimetre grid. Calculate the area of the parallelogram.

Area = base × height Area = 4 × 3 Area = 12cm 2

Example 5: Calculate the area of the parallelogram.

For the area calculation we use the perpendicular height (it must be straight up, not diagonal). The height of this parallelogram is 11 metres.

Area = base × height Area = 8 × 11 Area = 88m 2

A parallelogram is drawn on a centimetre grid. Calculate the area of the parallelogram.

Calculate the area of the parallelogram.

Finding the area of a trapezium

The image below shows a trapezium, a trapezium (trapezoid in American English) is a quadrilateral with two parallel sides.

The area of a trapezium = 1 ⁄ 2 (a + b) × height Where a and b are the lengths of the two parallel sides

This formula can be made by splitting the trapezium into a rectangle and a triangle (you don't have to know where the formula comes from, you just have to know the formula).

Example 6: Find the area of the trapezium

For the trapezium above: Area = 1 ⁄ 2 (6 + 10) × 7 Area = 1 ⁄ 2 (16) × 7 Area = 8 × 7 Area = 56 cm 2

A trapezium is drawn on a centimetre grid. Calculate the area of the trapezium.

Calculate the area of the trapezium.

The perimeter of a shape is the distance around the edge of the shape

To find the perimeter of a shape we add up the lengths of all of the sides

This rectangle has two sides with a length of 6cm and two sides with a length of 3cm

Perimeter = 6 + 6 + 3 + 3

Perimeter = 18 cm

Example 1: A rectangle is drawn on a centimetre grid Calculate the perimeter of the rectangle

Perimeter = 5 + 5 + 4 + 4 Perimeter = 18cm

Example 2: Calculate the perimeter of the triangle

Perimeter = 10 + 9 + 7 Perimeter = 26m

A rectangle is drawn on a centimetre grid. Calculate the perimeter of the rectangle.

Calculate the perimeter of the rectangle.

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Perimeter, area and volume

Lessons (16), checking understanding of perimeter, checking understanding of area, multiplicative relationships in circles, circumference of a circle, area of a circle, using the formula for the area of a circle, area of composite shapes, perimeter of composite shapes, finding a length in composite shapes, surface area of cuboids, properties of prisms, surface area of prisms, surface area of cylinders, volume of prisms, volume of cylinders, problem solving with perimeter, area and volume.