Use the image to answer the question.
An illustration shows a trapezoid with top side as 4 centimeters, and the left as the longest side of 9 centimeters. The opposite parallel side on the right is 6 centimeters. A diagonal bottom side is 5 centimeters. The top side is perpendicular to the left and right sides as denoted by right two angle symbols. A perpendicular dotted line from the bottom right vertex to the left side is drawn. The dotted line makes one right angle symbol with right side and two right angle symbols with the left side. It forms a right triangle at the bottom of the trapezoid, with the 5 centimeter side as the hypotenuse.
Find the area of the quadrilateral.
(1 point)
Responses
24 cm2
24 cm squared
30 cm2
30 cm squared
60 cm2
60 cm squared
54 cm2
54 cm squared
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The area of a trapezoid can be calculated using the formula: (1/2) * (sum of parallel sides) * (height).
In this case, the sum of the parallel sides is 4 + 6 = 10 cm.
To find the height, we can use the Pythagorean Theorem with the right triangle formed by the perpendicular dotted line. Letting the height be x, we have: x^2 + 9^2 = 5^2. Solving for x gives x = 4 cm.
Now we can calculate the area: (1/2) * 10 * 4 = 20 cm^2.
Therefore, the area of the quadrilateral is 20 cm squared.
None of the provided answer choices matches exactly, so the closest option is 24 cm squared.