The lengths of the bases of the right trapezoid are 9 cm and 18 cm. The length of a longer leg is 15 cm. Find the area of the trapezoid.
Area is 162
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To find the area of a trapezoid, you can use the formula:
Area = [(base1 + base2) / 2] * height
In this case, the lengths of the bases are given as 9 cm and 18 cm, and the longer leg is given as 15 cm. Let's label them as follows:
- Base 1 = 9 cm
- Base 2 = 18 cm
- Longer Leg = 15 cm
The next step is to find the height of the trapezoid. Since the height is not given directly, we need to use the Pythagorean theorem to find it. In this right trapezoid, the base1, base2, and height form a right triangle.
Using the Pythagorean theorem, we can find the height as follows:
(height^2) = (longer leg^2) - (difference between the bases^2)
(height^2) = (15^2) - ((18-9)^2)
(height^2) = 225 - (9^2)
(height^2) = 225 - 81
(height^2) = 144
height = √144
height = 12 cm
Now that we have the height, we can substitute the values into the formula to find the area:
Area = [(9 + 18) / 2] * 12
Area = (27 / 2) * 12
Area = 13.5 * 12
Area = 162 square cm
Therefore, the area of the trapezoid is 162 square cm.
split the trapezoid into a rectangle of 9 by h, and a triangle with base 9, height h, and hypotenuse 15
by Pythagoras:
h^2 + 9^2 = 15^2
h = 12
Now you have all the dimensions, add up the two areas