Answer:
233 in²
Explanation:
You want the area of the composite figure shown.
Area
The area is the sum of the areas of the parts. The parts include a triangle, and a rectangle with a missing corner.
Triangle area
The area of the triangle is given by the formula ...
A = 1/2bh
where b is the base and h is the height.
Here, we need to figure the missing dimension contributing to the height. The sum of right-side vertical line segments is 4 + 5 + 17 = 26. The bottom left vertical line segment is 6, so the height of the triangle is 26 -6 = 20.
The area of the triangle is ...
A = 1/2(12 in)(20 in) = 120 in²
Rectangle area
The overall dimensions of the rectangle at lower right are 17 in wide by (4+5) = 9 in tall. From that, a piece is removed that is 8 in wide by 5 in tall. The remaining area is ...
A = LW
A = (17 in)(9 in) -(8 in)(5 in) = (153 -40) in² = 113 in²
Blue area
The area shaded blue is the sum of the triangle area and the area of the notched rectangle:
total area = 120 in² +113 in² = 233 in²
The area of the figure is 233 square inches.
<95141404393>