The length of the bases of a right trapezoid are 9 cm and 18 cm. The length of the longer leg is 15 cm. Find the area of the trapezoid.
To find the area of a trapezoid, you can use the formula:
Area = (1/2) * (a + b) * h
where a and b are the lengths of the bases, and h is the height of the trapezoid.
In this case, a = 9 cm, b = 18 cm, and the longer leg is 15 cm. To find the height, we can use the Pythagorean theorem:
h^2 = 15^2 - ((18-9)/2)^2
h^2 = 225 - 22.5^2
h^2 = 225 - 101.25
h^2 = 123.75
h ≈ 11.11 cm
Now, we can plug the values into the area formula:
Area = (1/2) * (9 + 18) * 11.11
Area = (1/2) * 27 * 11.11
Area = 14.5 * 11.11
Area ≈ 159.72 cm^2
Therefore, the area of the trapezoid is approximately 159.72 square cm.