Use the image to answer the question.
An illustration shows a trapezoid with parallel sides on the left and right. The left side is 10 inches and right side is 16 inches. The top slanting side is labeled 7 inches. Two perpendicular dotted lines of 6 inches each are drawn from the top and bottom left vertices to the right side.
What is the area of the quadrilateral?
(1 point)
Responses
91 in.2
91 in. squared
39 in.2
39 in. squared
96 in.2
96 in. squared
78 in.2
78 in. squared
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page 9 of 9
To find the area of the quadrilateral, we can split it into two smaller shapes - a triangle and a parallelogram.
The area of the triangle is (1/2) * base * height.
The base of the triangle is 16 - 10 = 6 inches.
The height of the triangle is 6 inches.
Area of triangle = (1/2) * 6 * 6 = 18 square inches.
The area of the parallelogram is base * height.
The base of the parallelogram is 10 inches.
The height of the parallelogram is 6 inches.
Area of parallelogram = 10 * 6 = 60 square inches.
Therefore, the total area of the quadrilateral is the sum of the areas of the triangle and the parallelogram:
Total area = 18 + 60 = 78 square inches.
So, the area of the quadrilateral is 78 in.2.