Use the image to answer the question.
An illustration shows a trapezoid with top side as 4 centimeters, and the left as the longest side of 9 centimeters. The opposite parallel side on the right is 6 centimeters. A diagonal bottom side is 5 centimeters. The top side is perpendicular to the left and right sides as denoted by right two angle symbols. A perpendicular dotted line from the bottom right vertex to the left side is drawn. The dotted line makes one right angle symbol with right side and two right angle symbols with the left side. It forms a right triangle at the bottom of the trapezoid, with the 5 centimeter side as the hypotenuse.
Find the area of the quadrilateral.
(1 point)
Responses
24 cm2
24 cm squared
60 cm2
60 cm squared
54 cm2
54 cm squared
30 cm2
30 cm squared
Skip to navigation
The area of the quadrilateral can be found by splitting it into a triangle and a trapezoid.
First calculate the area of the triangle at the bottom by using the formula for the area of a triangle:
Area of triangle = 1/2 * base * height
Area of triangle = 1/2 * 6 * 3
Area of triangle = 9 cm squared
Now, calculate the area of the trapezoid by using the formula for the area of a trapezoid:
Area of trapezoid = 1/2 * sum of the lengths of the parallel sides * height
Area of trapezoid = 1/2 * (4 + 6) * 3
Area of trapezoid = 1/2 * 10 * 3
Area of trapezoid = 15 cm squared
Add the area of the triangle and the trapezoid together:
Total area = 9 + 15
Total area = 24 cm squared
Therefore, the area of the quadrilateral is 24 cm squared.