Area of Special Quadrilaterals Quick Check
3 of 53 of 5 Items
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
460 cm2
460 cm squared
220 cm2
220 cm squared
480 cm2
480 cm squared
240 cm2
240 cm squared
Skip to navigation
To find the area of the quadrilateral, we first have to find the height. The height is the perpendicular distance between the two parallel sides.
The height can be found using the Pythagorean Theorem on one of the right triangles formed by extending the perpendicular lines.
Let x be the height, then by the Pythagorean Theorem:
x^2 + 10^2 = 24^2
x^2 + 100 = 576
x^2 = 476
x ≈ √476
x ≈ 21.8 cm
Now that we have the height, we can find the area of the trapezoid using the formula:
Area = (1/2)(b1 + b2)h
Area = (1/2)(24 + 20)21.8
Area = (1/2)(44)(21.8)
Area ≈ 480 cm squared
Therefore, the correct answer is:
480 cm2
480 cm squared