To find the area of the trapezoid, we first need to find the height.
Using the Pythagorean theorem in the right triangle formed by the diagonal and the dotted line, we have:
5^2 = x^2 + 9^2
25 = x^2 + 81
x^2 = 25 - 81
x^2 = 56
x = √56
x ≈ 7.48 cm
Now, we can use the formula for the area of a trapezoid:
Area = (1/2) * (a + b) * h
Area = (1/2) * (4 + 6) * 7.48
Area = (1/2) * 10 * 7.48
Area = 37.4 square centimeters
Therefore, the area of the quadrilateral is 37.4 square centimeters.
Question
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)
1 answer
1 answer