Answer:
58 in²
Step-by-step explanation:
A horizontal line across the wide part of the pentagon will divide it into an upper triangle and a lower trapezoid. To find the area of the figure, you can use the formula for the area of a triangle (twice) and the formula for the area of a trapezoid.
A = 1/2bh . . . . area of triangle with base b and height h
A = 1/2(b1 +b2)h . . . . area of trapezoid with bases b1, b2, and height h
top triangle
The base is 6 in, the height is (8 -5) = 3 in. Its area is ...
A = 1/2(6 in)(3 in) = 9 in²
middle trapezoid
The bases are 4 in and 6 in, and the height is 5 in. Its area is ...
A = 1/2(4 in + 6 in)(5 in) = 25 in²
bottom triangle
The base is 8 in, and the height is 6 in. Its area is ...
A = 1/2(8 in)(6 in) = 24 in²
Then the area of the figure is ...
top triangle + trapezoid + bottom triangle
= 9 in² +25 in² +24 in² = 58 in² . . . . area of the figure
