Answer:
906 square feet
Explanation:
You want to know the area of the patio with the composite shape shown in the figure.
Composition
We can divide the shape into two trapezoids and one parallelogram. Each has a height of 12 ft.
The top trapezoid has bases of 13 ft and 23 ft. The parallelogram has a base of 23 ft. The bottom trapezoid has bases of 37 ft and 32 ft.
Area formulas
The relevant area formulas are ...
A = 1/2(b1 +b2)h . . . . . . area of a trapezoid
A = bh . . . . . . . . . . . . . area of a parallelogram
Computation
Working from the top down, the areas of the composite parts are ...
A = 1/2(13 +23)(12) = 6(36) = 216 . . . . square feet
A = (23)(12) = 276 . . . . square feet
A = 1/2(37 +32)(12) = 6(69) = 414 . . . . square feet
Then the total area of the walkway and patio is ...
216 +276 +414 = 906 . . . . square feet
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