Question

Use the formulas developed in this section to find the area of the trapezoid.

16 m
9.7 m
9 m
9.3 m
22 m

Answer 1

Interpret the two parallel sides (bases) as 22 m and 16 m, and the nonparallel sides (legs) as 9 m and 9.3 m. The area of a trapezoid is A = 1/2 (b1 + b2) h, so we need the height h.

Let the horizontal projections of the legs onto the longer base be x1 and x2, so x1 + x2 = 22 − 16 = 6. By the Pythagorean theorem,
h^2 + x1^2 = 9^2,
h^2 + x2^2 = 9.3^2,
with x2 = 6 − x1. Subtract the two equations:
9^2 − 9.3^2 = x1^2 − (6 − x1)^2 = 12x1 − 36.
Compute the left side: 81 − 86.49 = −5.49, so
12x1 − 36 = −5.49 ⇒ 12x1 = 30.51 ⇒ x1 = 2.5425 m.

Then h^2 = 9^2 − x1^2 = 81 − (2.5425)^2 = 81 − 6.46430625 = 74.53569375,
so h ≈ sqrt(74.53569375) ≈ 8.633 m.

Finally,
A = 1/2 (22 + 16) · 8.633 = 19 · 8.633 ≈ 164.03 m^2.

Answer: approximately 164.0 m^2.