The area of the compound figure can be calculated as the sum of smaller areas of known shapes, as shown below:
There are 3 rectangles and one triangle.
The first rectangle has dimensions of 19 ft by 7 ft. Area = 19 ×7 = 133 sq ft
The second rectangle has dimensions of 6 ft by 11 ft. Area = 6 ×11 = 66 sq ft
The third rectangle has a width of 7 ft and a length of 4 + 6 + 3 = 13 ft. Area = 7 ×13 = 91 sq ft
The value of x can be obtained by subtracting the length of the third rectangle minus 7 ft: x = 13 - 7 = 6 ft
The base of the triangle is b = x + 5 = 11 ft
The height of the triangle is h = 5 ft
The area of the triangle is:
[tex]A=\frac{11\cdot5}{2}=27.5\text{ sq ft}[/tex]
The total area of the figure is 133 + 66 + 91 + 27.5 = 317.5 sq ft
