Perimeter and area.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Perimeter and area

Area and volume

Lesson 1 of 7

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Before We Start

Area and volume

Lesson 1 of 7

Answer each one, then check.

1

What is the perimeter of a 7 cm by 4 cm rectangle?

2

What is the area of a 7 cm by 4 cm rectangle?

3

Work out ½ × 9 × 6.

4

Solve 4h = 24.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Before We Start - Answers

Area and volume

Lesson 1 of 7

1

What is the perimeter of a 7 cm by 4 cm rectangle?

22 cm

2

What is the area of a 7 cm by 4 cm rectangle?

28 cm²

3

Work out ½ × 9 × 6.

27

4

Solve 4h = 24.

h = 6

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Area and volume

Lesson 1 of 7

1

Find the perimeter of 2D shapes, including compound shapes.

2

Use the area formulae for rectangles, triangles, parallelograms and trapeziums.

3

Find the area of a compound shape.

4

Work backwards from an area to a missing length.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

The Area Formulae

Area and volume

Lesson 1 of 7

Every height is the perpendicular height - at right angles to the base.

A parallelogram is a rectangle with a triangle moved from one end to the other, so its area is base × height. A triangle is half a parallelogram. A trapezium's area uses the mean of its parallel sides: ½(a + b)h.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Perimeter and Area

Area and volume

Lesson 1 of 7

Perimeter is the distance round the edge; area is the space inside.

Perimeter

Add every side. Units: cm, m.

Area

Count squares or use a formula. Units: cm², m².

Perpendicular height

Use the height at right angles to the base, NOT the slanted side.

Same units

Change all the lengths into the same unit before you calculate.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Area of a Trapezium

Area and volume

Lesson 1 of 7

A trapezium has parallel sides of 6 cm and 10 cm. The perpendicular distance between them is 5 cm. Work out its area.

1

Write the formula

A = ½(a + b)h

2

Substitute

A = ½(6 + 10) × 5

3

Calculate

½ × 16 × 5 = 40

ANSWER

40 cm²

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

A Compound Shape

Area and volume

Lesson 1 of 7

An L-shape is made by cutting a 4 cm by 3 cm rectangle from one corner of a 10 cm by 8 cm rectangle. Work out its area and its perimeter.

1

Area: big rectangle minus the cut-out

10 × 8 − 4 × 3 = 80 − 12 = 68

2

Perimeter: the sides are 10, 5, 4, 3, 6 and 8

10 + 5 + 4 + 3 + 6 + 8 = 36

3

Notice

Cutting a corner out leaves the perimeter the same as the rectangle's: 2(10 + 8) = 36

ANSWER

Area 68 cm², perimeter 36 cm

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Working Backwards

Area and volume

Lesson 1 of 7

A triangle has an area of 24 cm² and a base of 8 cm. Work out its perpendicular height.

1

Write the formula

24 = ½ × 8 × h

2

Simplify

24 = 4h

3

Solve

h = 6

ANSWER

6 cm

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Common Mistakes

Area and volume

Lesson 1 of 7

WRONG

• Using the slanted side as the height of a parallelogram.

• Forgetting the ½ for a triangle.

• Mixing cm and m in one calculation.

• Writing area in cm.

RIGHT

• Use the perpendicular height.

• Triangle: ½ × b × h.

• Convert to one unit first.

• Area is always in square units: cm², m².

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Key Terms

Area and volume

Lesson 1 of 7

Perimeter

The total distance around the edge of a shape.

Area

The amount of space inside a 2D shape, in square units.

Perpendicular height

The height measured at right angles to the base.

Compound shape

A shape made from two or more simple shapes.

Trapezium

A quadrilateral with one pair of parallel sides.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Area and volume

Lesson 1 of 7

YOUR TASK

Same Area, Different Shape

10 minutes

Draw as many different shapes as you can with an area of exactly 24 cm²: a rectangle, a triangle, a parallelogram and a trapezium. Label the dimensions of each. Which of your shapes has the smallest perimeter?

1

Choose a base.

2

Work out the height needed.

3

Compare the perimeters.

WHAT A GOOD ANSWER SHOWS

For example: rectangle 6 by 4; triangle base 8, height 6; parallelogram base 6, height 4; trapezium with parallel sides 5 and 7 and height 4. Of the rectangles, the one closest to a square (about 4.9 by 4.9) has the smallest perimeter.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Can I...?

Area and volume

Lesson 1 of 7

Find the perimeter of a shape.

Find the area of a rectangle and a triangle.

Find the area of a parallelogram and a trapezium.

Find missing sides of a compound shape.

Find the area of a compound shape.

Find a missing length from an area.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

Rectangle lw; triangle ½bh; parallelogram bh; trapezium ½(a + b)h.

Heights are always perpendicular.

Compound shapes: split, or subtract a missing part.

Area units are squared.

EXAM FOCUS

A wall is 4 m long and 2.5 m high. It has a door 0.8 m wide and 2 m high. The wall needs two coats of paint. One tin covers 5 m². How many tins are needed? (4 marks)

In a problem, write down what each number you calculate represents - "area of wall", "area to paint" - so the examiner can follow you and give process marks.

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