A trapezium has an area of 90 cm2. Its parallel sides are 7 cm and 13 cm. Find the perpendicular distance between them.
- Area = 1/2 × (a + b) × h, so 90 = 1/2 × (7 + 13) × h.
- 90 = 1/2 × 20 × h = 10h.
- h = 90 ÷ 10 = 9.
Answer: 9 cm
Area and perimeter
Maths · Mensuration. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
The perimeter is the distance all the way round a shape. Add every side, and give the answer in units of length such as cm. The area is the amount of surface inside the shape, in square units such as cm2.
Every area formula uses a perpendicular height: the height measured at 90° to the base. A sloping side is used for the perimeter, not for the area.
Some questions work backwards: they give the area and ask for a side or a height. Write the formula, put in the numbers you know and solve. For a shape made of several parts, or a path around a shape, add or subtract simple areas.
Rules to remember
- Rectangle: area = length × width; perimeter = 2 × (length + width)
- Triangle: area = 1/2 × base × perpendicular height
- Parallelogram: area = base × perpendicular height
- Trapezium: area = 1/2 × (sum of the parallel sides) × perpendicular distance between them (A = 1/2 × (a + b) × h)
- Rhombus or kite: area = 1/2 × (product of the diagonals)
- Square: side = perimeter ÷ 4; area = side2
- Path or border: area = area of the outer shape − area of the inner shape
Common mistake
Students multiply the two sides of a parallelogram, or use the sloping side of a triangle as its height. Use the perpendicular height every time.
Worked example
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