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
480 cm2
480 cm squared
460 cm2
460 cm squared
240 cm2
240 cm squared
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The area of the quadrilateral can be calculated by finding the area of the trapezoid and then subtracting the area of the two right triangles formed by the perpendicular lines.
Area of trapezoid = (1/2)(sum of parallel sides)(height)
Area of trapezoid = (1/2)(24 + 20)(10)
Area of trapezoid = (1/2)(44)(10)
Area of trapezoid = 220 cm^2
Area of right triangle = (1/2)(base)(height)
Area of right triangle = (1/2)(20)(10)
Area of right triangle = 100 cm^2
Total area of quadrilateral = Area of trapezoid - 2(Area of right triangle)
Total area of quadrilateral = 220 - 2(100)
Total area of quadrilateral = 220 - 200
Total area of quadrilateral = 20 cm^2
Therefore, the correct answer is 240 cm^2.