Use Area to Solve Problems Quick Check
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Question
Use the image to answer the question.
An illustration shows a trapezoid with shorter base of length 36 and the opposite longer side of length 48. The legs on the left and right sides are of length 21. The perpendicular height from the bottom left vertex to the longer side is 18. The length between the top left vertex of the longer side and the point where the height meets the longer side is labeled 6. The height is shown in a dashed line.
Compose a rectangle to help find the area of a trapezoid-shaped tabletop in square inches. What is the area of the tabletop?
(1 point)
Responses
648 square inches
648 square inches
756 square inches
756 square inches
882 square inches
882 square inches
864 square inches
864 square inches
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To find the area of a trapezoid, we use the formula: \( Area = \frac{1}{2} \times (b1 + b2) \times h \), where \( b1 \) and \( b2 \) are the lengths of the two parallel sides, and \( h \) is the height.
In this case:
\( b1 = 36 \)
\( b2 = 48 \)
\( h = 18 \)
Plugging in the values:
\( Area = \frac{1}{2} \times (36 + 48) \times 18 \)
\( Area = \frac{1}{2} \times 84 \times 18 \)
\( Area = 42 \times 18 \)
\( Area = 756 \)
Therefore, the area of the tabletop is 756 square inches.
Therefore, the correct answer is:
756 square inches