Areas of parallelograms, triangles and trapeziums · Usually met around P5
From an area back to a base or height
Triangle: height = area × 2 ÷ base.
How to do it
Method
Triangle: height = area × 2 ÷ base
Area 24, base 6: 24 × 2 ÷ 6 = 8
Another way
An equation
6 × x ÷ 2 = 24, x = 8
In full
Write the formula, then work it backwards. Parallelogram: area = base × height, so height = area ÷ base. Triangle: area = base × height ÷ 2, so height = area × 2 ÷ base; don't forget the × 2. Trapezium: area = (top + bottom) × height ÷ 2, so height = area × 2 ÷ (top + bottom), and top = area × 2 ÷ height − bottom. Or write the unknown as x and solve: x × 6 ÷ 2 = 24. Check by putting the answer back into the formula.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The parallelogram's area is 285 cm². How many centimetres is its base?
Show the answer and working
Answer: 19 cm
Base = area ÷ height = 285 ÷ 15 = 19.
Example 2
A triangle has base 11 cm and height 15 cm. What part of a parallelogram with the same base and height is its area?
- A. Twice
- B. A quarter
- C. The same
- D. Half
Choose the right answer
Show the answer and working
Answer: D. Half
Triangle 11 × 15 ÷ 2, parallelogram 11 × 15: the triangle is half.
Example 3
The trapezium's area is 75 cm². How many centimetres is its top?
Show the answer and working
Answer: 5 cm
Top + bottom = 75 × 2 ÷ 6 = 25; top = 25 − 20 = 5.
Practise it in the game →Areas of parallelograms, triangles and trapeziums · Free to start, unlimited questions, no download