Question

A composite figure is represented in the image.

A six-sided composite figure. A vertical line on the left is labeled 4 meters. The base is labeled 9 meters. There is a small portion from the vertical line that is parallel to the base that is labeled 3 meters. This portion leads to two segments that come to a point, and from that point, there is a height of 3 meters labeled.

What is the total area of the figure?

a: 75 m2
b: 63 m2
c: 61.5 m2
d: 45 m2

Answer 1

The total area of the figure is 63 m².

To find the area of the figure, we need to break it down into simpler shapes. The figure consists of a trapezoid and a right triangle.

The area of the trapezoid is [(base1 + base2) / 2] x height.
The two bases of the trapezoid are 4 m and 9 m + 3 m = 12 m. The height of the trapezoid is 3 m.

Area of the trapezoid = [(4 + 12) / 2] x 3 = 48 m².

The area of the right triangle is (base x height) / 2.
The base of the triangle is 3 m and the height is 3 m.

Area of the triangle = (3 x 3) / 2 = 4.5 m².

The total area of the figure is the sum of the area of the trapezoid and the area of the triangle.

Total area = 48 + 4.5 = 52.5 m².

Therefore, the closest option is c: 61.5 m².