EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Perimeter and area
Area and volume · Lesson 1 of 7
Before We Start
Answer each one, then check.
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
Learning Objectives
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.
The Area Formulae
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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. |
Every height is the perpendicular height - at right angles to the base. |
Perimeter and Area
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.
Area of a Trapezium
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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
A Compound Shape
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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
Working Backwards
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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
Common Mistakes
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WRONG |
RIGHT |
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▸ 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. |
▸ Use the perpendicular height. ▸ Triangle: ½ × b × h. ▸ Convert to one unit first. ▸ Area is always in square units: cm², m². |
Key Terms
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Perimeter The total distance around the edge of a shape. |
Area The amount of space inside a 2D shape, in square units. |
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Perpendicular height The height measured at right angles to the base. |
Compound shape A shape made from two or more simple shapes. |
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Trapezium A quadrilateral with one pair of parallel sides. |
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Your Task: Same Area, Different Shape
10 minutes
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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. |
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.
Can I...?
☐ 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.
Summary
✓ 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.
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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. |