Use the image to answer the question.
An illustration shows a trapezoid with parallel sides on the top and bottom. The top side is 24 centimeters and bottom side is 20 centimeters. Two perpendicular dotted lines of 10 centimeters are drawn from the bottom vertices to the top side. The two perpendicular lines are denoted by 4 right angle symbols.
What is the area of the quadrilateral?
(1 point)
Responses
220 cm2
220 cm squared
240 cm2
240 cm squared
460 cm2
460 cm squared
480 cm2
480 cm squared
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To find the area of the quadrilateral, we need to find the area of the trapezoid and subtract the area of the two triangles formed by the perpendicular lines.
The area of the trapezoid is calculated as (1/2) * (sum of parallel sides) * (height)
Area = (1/2) * (20 + 24) * 10
Area = (1/2) * 44 * 10
Area = 220
The area of each triangle is calculated as (1/2) * base * height
Area of one triangle = (1/2) * 20 * 10
Area of one triangle = 100
Since there are two triangles, the total area of the triangles is 200.
Thus, the total area of the quadrilateral is:
220 (trapezoid) - 200 (two triangles) = 20 cm squared
Therefore, the correct answer is:
220 cm2