Find the area of the trapezoid

B) 32√3 ft²

x = √8² - (4√3)²

= √64 - 48

= √16

= 4 ft

b = B - x = 10ft - 4ft = 6 ft

A = (b + B)×h/2

= (6 + 10)×4√3/2

= 16×2√3

= 32√3 ft²

32 ft²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = h (a + b)

where h is the height and a, b the parallel bases

We require to calculate the base of the right triangle using Pythagoras' identity.

let x be the base , then

x² + (4 )² = 8² , that is

x² + 48 = 64 ( subtract 48 from both sides )

x² = 16 ( take the square root of both sides )

x = = 4

Thus the top base = 10 - 4 = 6 ft

Hence

A = × 4 × (10 + 6)

   = 2 × 16

    = 32 ft²