Answer:
84 square inches
Explanation:
You want to know the area of the given composite shape.
Decomposition
The 7-inch line can be extended 5 inches to the right to cut the shape into two parts:
- upper rectangle 5 inches wide and 6 inches high
- lower trapezoid with bases 12 inches and 15 inches, and 4 inch height
Area formulas
The formulas for the areas of these pieces are ...
A = bh . . . . . rectangle with base b and height h
A = 1/2(b1 +b2)h . . . . trapezoid with bases b1 and b2, and height h
Application
The area of the upper rectangle is ...
A = (5 in)(6 in) = 30 in²
The area of the lower trapezoid is ...
A = 1/2(12 in +15 in)(4 in) = 54 in²
Total area
The total area of the figure is the sum of the areas of its parts:
figure area = rectangle area + trapezoid area
= 30 in² +54 in² = 84 in²
The area of the figure is 84 in².