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An international football pitch is 105m x 68m.

Level 3-4 Shapes - Perimeter and Area

Explore perimeter and area of rectangles, triangles, and compound shapes. Use formulas, units, and conversions to solve practical problems about fencing, flooring, and tiling.

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Fascinating Fact:

If each solar panel on a roof is 2 metres by 1 metre, and the roof area is 40 square metres, you could fit 20 panels.

In KS3 Maths, perimeter measures the distance around a shape and area measures the space inside it. You will apply formulas for rectangles, triangles, and compound shapes, choose sensible units, and convert between cm, m, and km where needed.

Key Terms

Perimeter: The total distance around the edge of a 2D shape.
Area: The amount of flat surface a shape covers, measured in square units such as cm² or m².
Compound shape: A shape made by joining simple shapes; find its area by splitting it into rectangles/triangles.

Frequently Asked Questions (Click to see answers)

What is the formula for the area of a triangle?

The area of a triangle is ½ × base × height. The height must be perpendicular to the base. Example: base 8 cm, height 5 cm gives 20 cm².

How do I work out the perimeter of a compound shape?

Add the lengths around the outside edge only. If a side is missing, use other dimensions to deduce it before adding all outer sides together.

Which units should I use for perimeter and area?

Perimeter uses linear units (mm, cm, m, km). Area uses squared units (mm², cm², m²). Convert units before calculating if measurements differ.

Try These Related Quizzes

1 .

What is the area of a rectangle with a length of 9 cm and a width of 7 cm?

49 cm²

54 cm²

63 cm²

77 cm²

9 x 7 = 63

2 .

A rectangle is 2 metres long and 88 centimetres wide; what is its area?

0.176 metres²

1.76 metres²

3.52 metres²

176 metres²

Don't mix up the metres and centimetres mentioned in the question

3 .

If a square has sides that are 13 cm long, what is its area?

26 cm²

52 cm²

105 cm²

169 cm²

13cm x 13cm = 169cm²

4 .

Which of the following shapes would you not be asked to find the perimeter or area of?

Rectangle

Sphere

Trapezium

Triangle

A sphere is a 3 dimensional shape. Remember that perimeter and area are only associated with 2 dimensional shapes

5 .

A rectangle has a length that is twice its width. If the length is 18 m, what is its perimeter?

36 m

48 m

54 m

72 m

The width of the rectangle must be 9 m

6 .

What is the perimeter of a rectangle with a length of 28 cm and a width of 16 cm

42 cm

64 cm

74 cm

88 cm

(28 x 2) + (16 x 2) = 56 + 32 = 88

7 .

Which of the following is not a valid measurement for an area?

102 m²

15 m

18 mm²

52 cm²

Area is always spoken of in terms of 'square' units i.e. 18 square millimetres or 52 square centimetres. In the answers above, 15 m is only a length

8 .

What is the area of a square that has a length of 15 cm and a width of 16 cm?

225 cm²

256 cm²

240 cm²

Not a valid question

If the sides are different sizes then it cannot be a square!

9 .

To calculate the area of a rectangle it is necessary to multiply the length by the width; how is this formula usually represented?

A = l x w

e = mc²

L = a/w

W = a/l

Area = length x width

10 .

An international football pitch is 105 m x 68 m. What is the area of one half of the pitch?

3,570 metres²

4,624 metres²

7,140 metres²

11,025 metres²

105m x 68m = 7,140 metres² so half the pitch's area is 7,140 metres² ÷ 2 = 3,570 metres²

You can find more about this topic by visiting BBC Bitesize - Perimeter, Area, Volume

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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