Area of Special Quadrilaterals Quick Check
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Question
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
96 in.2
96 in. squared
91 in.2
91 in. squared
39 in.2
39 in. squared
78 in.2
78 in. squared
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To find the area of the quadrilateral, we need to divide it into two triangles and a rectangle.
First, we need to find the height of the trapezoid. Since the dotted lines form a right triangle with the height as one leg and 6 inches and 10 inches as the other two legs, we can use the Pythagorean theorem to find the height.
10^2 = 6^2 + h^2
100 = 36 + h^2
h^2 = 64
h = 8 inches
Next, we can find the area of the trapezoid:
Area = (1/2) * (sum of the bases) * height
Area = (1/2) * (10 + 16) * 8
Area = (1/2) * 26 * 8
Area = 104 square inches
Therefore, the area of the quadrilateral is 104 square inches. None of the given responses match the correct answer, so the correct answer would be 104 in.².