Answer:
[tex]\large\boxed{A=54\ m^2}[/tex]
Step-by-step explanation:
The formula of an area of a trapezoid:
[tex]A=\dfrac{b_1+b_2}{2}\cdor h[/tex]
b₁, b₂ - bases
h - height
We must use the Pythagorean theorem:
[tex]x^2+8^2=10^2[/tex]
[tex]x^2+64=100[/tex] subtract 64 from both sides
[tex]x^2=36\to x=\sqrt{36}\\\\x=6\ m[/tex]
We have b₁ = 6 + 6 = 12m, b₂ = 6m and h = 8m.
Substitute:
[tex]A=\dfrac{12+6}{2}\cdot6=\dfrac{18}{2}\cdot6=(9)(6)=54\ m^2[/tex]
