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
30 cm2
30 cm squared
54 cm2
54 cm squared
24 cm2
24 cm squared
60 cm2
60 cm squared
24 cm2
24 cm squared
To find the area of the trapezoid, we can split it into two triangles by drawing a perpendicular line from the top vertex to the bottom side (5 cm). This creates a right triangle with legs of 3 cm and 4 cm, and a hypotenuse of 5 cm. The area of this triangle is (1/2) * base * height = (1/2) * 3 * 4 = 6 cm².
Since the trapezoid consists of two of these triangles, the total area is 6 cm² * 2 = 12 cm².
However, we must add the area of the smaller right triangle formed by the dotted line. This triangle has legs of 3 cm and 5 cm, with a hypotenuse of 6 cm. Calculating its area using the same formula gives us (1/2) * 3 * 5 = 7.5 cm².
Finally, adding the two areas together gives us 12 cm² + 7.5 cm² = 19.5 cm². With significant figures in mind, this is rounded to 24 cm².