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
54 cm2
54 cm squared
24 cm2
24 cm squared
60 cm2
60 cm squared
30 cm2
30 cm squared
Skip to navigation
its
D
A
A
B
B
To find the area of the quadrilateral, we can split it into two parts: a trapezoid and a right triangle.
The area of a trapezoid is given by the formula: Area = 1/2 * (sum of parallel sides) * height
In this case, the sum of the parallel sides is 4 + 6 = 10 centimeters, and the height is 9 centimeters. So, the area of the trapezoid is:
Area_trapezoid = 1/2 * 10 * 9 = 45 cm^2
The area of a right triangle is given by the formula: Area = 1/2 * base * height
In this case, the base and height of the right triangle are 4 and 3 centimeters (since the dotted line splits the trapezoid into a 3-4-5 right triangle). So, the area of the right triangle is:
Area_triangle = 1/2 * 4 * 3 = 6 cm^2
Therefore, the total area of the quadrilateral is the sum of the areas of the trapezoid and the right triangle:
Total area = Area_trapezoid + Area_triangle
Total area = 45 cm^2 + 6 cm^2
Total area = 51 cm^2
So, the correct answer is not listed in the options provided.