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
78 in.2
78 in. squared
91 in.2
91 in. squared
96 in.2
96 in. squared
39 in.2
39 in. squared
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To find the area of the quadrilateral, first calculate the area of the trapezoid formed by the 10-inch left side, 16-inch right side, and top slanting side of 7 inches.
Area of a trapezoid = 1/2 * (sum of parallel sides) * height
Area = 1/2 * (10 + 16) * 7
Area = 1/2 * 26 * 7
Area = 91 square inches
Next, calculate the area of the two right triangles formed by the dotted lines.
Area of each right triangle = 1/2 * base * height
Area = 1/2 * 6 * 6
Area = 18 square inches (for each triangle)
Since there are two right triangles, the combined area of both triangles is 18 + 18 = 36 square inches.
To find the total area of the quadrilateral, add the area of the trapezoid and the area of the two triangles:
91 + 36 = 127 square inches
Therefore, the correct answer is not provided in the options given.