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
A 480 cm^2
B 240 cm^2
C 220 cm^2
D 460 cm^2
B 240 cm^2
To find the area of the quadrilateral, you can split it into a rectangle and two right triangles.
First, find the area of the rectangle by multiplying the base (20 cm) by the height (10 cm), which equals 200 cm^2.
Then, find the area of the two right triangles by multiplying the base (10 cm) by the height (10 cm) and dividing by 2, since it's a right triangle. This comes out to 50 cm^2 per triangle, so 50 cm^2 x 2 = 100 cm^2.
Adding the area of the rectangle and the two triangles together, you get 200 cm^2 + 100 cm^2 = 300 cm^2.
Therefore, the area of the quadrilateral is 300 cm^2, which is option B.