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. 240 cm^2
2. 480 cm^2
3. 460 cm^2
4. 220 cm^2
The area of a trapezoid can be calculated using the formula: (1/2) * (sum of the lengths of the parallel sides) * (distance between the parallel sides).
In this case, the sum of the lengths of the parallel sides is 24 cm + 20 cm = 44 cm. The distance between the parallel sides can be calculated using the Pythagorean theorem: sqrt(10^2 + (24-20)^2) = sqrt(100 + 16) = sqrt(116) = 2sqrt(29) cm.
Therefore, the area of the quadrilateral is (1/2) * 44 cm * 2sqrt(29) cm = 44 * sqrt(29) cm^2 ≈ 220 cm^2.
So, the correct answer is:
4. 220 cm^2