Area and Perimeter
Perimeter is the total distance around the outside edge of a 2D shape. Area is the amount of flat space a 2D shape covers, measured in square units such as cm^2 or m^2.
Before you start
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Method
- For perimeter, add together the lengths of all the sides of the shape; if a side length is missing, use the fact that opposite sides of a rectangle are equal to work it out.
- For a rectangle, area = length x width.
- For a triangle, area = 1/2 x base x perpendicular height.
- For a parallelogram, area = base x perpendicular height.
- For a trapezium, area = 1/2 x (sum of the parallel sides) x perpendicular height.
- For a compound shape, split it into rectangles and triangles you know how to handle, find each area separately, then add or subtract them to get the total.
Worked example
A trapezium has parallel sides of 6 cm and 10 cm, and a perpendicular height of 4 cm. Find its area.
- Use the trapezium formula: area = 1/2 x (a + b) x h.
- Add the parallel sides: 6 + 10 = 16.
- Multiply by the height: 16 x 4 = 64.
- Multiply by 1/2: 64 x 1/2 = 32.
- The area is 32 cm^2.
Practice questions
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Exam-style questions
Written in the style of a GCSE exam paper, with a full mark scheme.
A garden is a rectangle 14 m long and 9 m wide, with a triangular flower bed of base 6 m and height 4 m removed from one corner. Work out the remaining area of the garden.
A compound shape is made from a rectangle 10 cm by 6 cm with a semicircle of diameter 6 cm attached to one of the shorter sides. Work out the total area, giving your answer to 1 decimal place. Use pi = 3.14.
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