Answer:
36*sqrt(3)
Explanation:
Remark
Use the Pythagorean theory to find the height. Use that height to find the area of the rectangle and the triangle Or
You can find the area of the trapezoid which requires only 1 step after you find the height.
Height
c = 8
b = 4
a = ?
a^2 + b^2 = c^2
a^2 + 4^2 = 8^2
a^2 + 16 = 64
a^2 = 64 - 16
a^2 = 48
a^2 = 16 * 3
sqrt(a^2) = sqrt(16*3)
a = 4 * sqrt(3)
That's the height
Trapezoid
b1 = 7
b2 = 7 + 4 = 11
h = 4*sqrt(3)
Area = (b1 + b2)*h / 2
Area = (7 + 11)* 4*sqrt(3)/2
Area = 18 * 2 sqrt(3)
Area = 36* sqrt(3)