To find the area of the quadrilateral, we first need to find the area of the trapezoid and then subtract the area of the two right triangles formed by the perpendicular lines.
The formula for the area of a trapezoid is:
Area = 1/2 * (sum of parallel sides) * height
In this case, the sum of the parallel sides is 24 + 20 = 44 cm, and the height is 10 cm. So the area of the trapezoid is:
Area of trapezoid = 1/2 * 44 cm * 10 cm = 220 cm²
Now, we need to subtract the area of the two right triangles. Since each triangle has a base of 20 cm and a height of 10 cm, the area of one triangle is:
Area of one triangle = 1/2 * 20 cm * 10 cm = 100 cm²
Since there are two triangles, the total area of the two triangles is 2 * 100 cm² = 200 cm².
Therefore, the area of the quadrilateral is:
220 cm² - 200 cm² = 20 cm²
So the correct answer is:
220 cm²
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 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
240 cm2
240 cm squared
480 cm2
480 cm squared
460 cm2
460 cm squared
220 cm2
220 cm squared
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1 answer