Area and Perimeter of a Trapezoid

Area: $A = \dfrac{(5 + 9)}{2} \times 4 = \dfrac{14}{2} \times 4 = 7 \times 4 = 28 \text{ cm}^2$

Perimeter: $P = 5 + 9 + 5 + 5 = 24 \text{ cm}$

A swimming pool has a trapezoidal cross-section. The shallow end is 1.2 m deep and the deep end is 2.8 m deep. The pool is 25 m long.

Treating the cross-section as a trapezoid with $a = 1.2\text{ m}$, $b = 2.8\text{ m}$, $h = 25\text{ m}$:

$A = \dfrac{(1.2 + 2.8)}{2} \times 25 = 2 \times 25 = 50 \text{ m}^2$

Multiplying this cross-sectional area by the pool's width gives the total volume of water — useful for calculating heating costs and chemical dosing.

A farmer's field has two parallel sides of 80 m and 120 m, with a perpendicular distance of 60 m between them.

$A = \frac{(80 + 120)}{2} \times 60 = 100 \times 60 = 6000 \text{ m}^2$

That is 0.6 hectares. At a typical wheat yield of 8 tonnes per hectare, the field could produce $0.6 \times 8 = 4.8$ tonnes — useful for planning fertiliser quantities and estimating income.

A dam has a trapezoidal cross-section with a top width of 6 m, a base width of 20 m, and a height of 12 m.

$A = \frac{(6 + 20)}{2} \times 12 = 13 \times 12 = 156 \text{ m}^2$

If the dam is 200 m long, the volume of concrete needed is $156 \times 200 = 31200 \text{ m}^3$. Civil engineers calculate this to estimate material costs and structural load before construction begins.