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 cm2
To find the area of the trapezoid, we can divide it into two shapes: a trapezoid and a right triangle.
1. Area of the trapezoid = [(b1 + b2) * h] / 2
Where b1 and b2 are the lengths of the top and bottom bases, and h is the height.
In this case, the top base (b1) = 4 cm, the bottom base (b2) = 6 cm, and the height (h) = 5 cm.
Area of the trapezoid = [(4 + 6) * 5] / 2 = (10 * 5) / 2 = 50 / 2 = 25 cm2
2. Area of the right triangle = (base * height) / 2
The base of the triangle = 6 cm and the height = 5 cm.
Area of the triangle = (6 * 5) / 2 = 30 / 2 = 15 cm2
3. Total area of the quadrilateral = Area of trapezoid + Area of right triangle
Total area = 25 cm2 + 15 cm2 = 40 cm2
Therefore, the area of the quadrilateral is 30 cm2.