Question

Find the area of the trapezoid.

Answer 1

`\large\boxed{A=54\ m^2}`

Explanation:

The formula of an area of a trapezoid:

`A=(b_1+b_2)/(2)\cdor h`

b₁, b₂ - bases

h - height

We must use the Pythagorean theorem:

`x^2+8^2=10^2`

`x^2+64=100` subtract 64 from both sides

`x^2=36\to x=√(36)\\\\x=6\ m`

We have b₁ = 6 + 6 = 12m, b₂ = 6m and h = 8m.

Substitute:

`A=(12+6)/(2)\cdot6=(18)/(2)\cdot6=(9)(6)=54\ m^2`