Find the area of the trapezoid. Leave your answer in simplest radical form. The figure is not drawn to scale.
A trapezoid is shown. Its shorter base is at the top of the image and its length is 12 centimeters. The trapezoid’s height is 6 centimeters. Vertical dotted lines are drawn through the trapezoid dividing it into two right triangles and a rectangle. The triangle on the left side of the trapezoid has an angle at the bottom left corner labeled 45 degrees. The triangle on the right side of the trapezoid has its horizontal side at the bottom of the triangle labeled 2 centimeters.
(1 point)
Responses
84 cm^2
96 cm^2
72 cm^2
108 cm^2
To find the area of the trapezoid, we need to find the area of the two triangles and the rectangle separately and then add them together.
The area of the left triangle is 1/2 * base * height = 1/2 * 6 * 6 = 18 cm^2
The area of the right triangle is 1/2 * base * height = 1/2 * 2 * 6 = 6 cm^2
The area of the rectangle is base * height = 12 * 6 = 72 cm^2
Adding all three areas together:
18 cm^2 + 6 cm^2 + 72 cm^2 = 96 cm^2
Therefore, the area of the trapezoid is 96 cm^2.