The area of a trapezium is A=12(a+b)h.
You do not need to know this, but this is why it works:
Fit two trapezia together, side by side, to make a parallelogram. One of the parallelograms needs to be flipped.
The area of a parallelogram is base x perpendicular height. For this parallelogram, area=(a+b)×height.
The parallelogram is equal to two trapezia, therefore the area of one trapezium is A=12(a+b)h
What is the area of the trapezium, shown below?
| Area of Trapezium | = 12(a + b) x h | |
| Substitute | A | =12(14+20)×10 |
| Divide both sides by 20 | A | =170 |
Answer: 170 cm2
The parallel sides of a trapezium are 18 and 22 cm long. The area of the trapezium is 400 cm2. What is the perpendicular height of the trapezium?
| Area of Trapezium | = 12(a + b) x h | |
| Substitute | 400 | =12(18+22)h |
| 400 | =20h | |
| Divide both sides by 20 | 20 | =h |
Answer: 2.2 cm