Given: KLMN is a trapezoid, m∠K = 90°, LM = 9, KN = 18, MN = 15.
Find: Area of KLMN
Please I really need help!!!!
drop an altitude from M to P on KN.
Then PM = √(15^2-9^2) = 12
the area is thus (9+18)/2 * 12
To find the area of the trapezoid KLMN, we can use the formula for the area of a trapezoid:
Area = (base1 + base2) * height / 2
In this case, since KLMN is a trapezoid with a right angle at K, we can label the bases as follows:
base1 = LM = 9
base2 = KN = 18
The height of the trapezoid is the distance between the bases, which is MN = 15.
Using the formula, we can now calculate the area.
Area = (base1 + base2) * height / 2
= (9 + 18) * 15 / 2
= 27 * 15 / 2
= 405 / 2
= 202.5
Therefore, the area of trapezoid KLMN is 202.5 square units.
To find the area of trapezoid KLMN, we can use the formula:
Area = (1/2) * (sum of the parallel sides) * (height)
First, let's label the parallel sides. In trapezoid KLMN, LM is parallel to KN. Therefore, the parallel sides are LM and KN.
Next, we need to find the height of the trapezoid. We are not given the height directly, but we can find it using the Pythagorean theorem.
Given that m∠K = 90°, we have a right triangle KLM. The sides LM and KM are given, with LM = 9 and KM = 15.
Using the Pythagorean theorem, we can find the height as follows:
height^2 = KM^2 - LM^2
height^2 = 15^2 - 9^2
height^2 = 225 - 81
height^2 = 144
height = √144
height = 12
Now that we have the height, we can calculate the area:
Area = (1/2) * (LM + KN) * (height)
Area = (1/2) * (9 + 18) * 12
Area = (1/2) * 27 * 12
Area = (1/2) * 324
Area = 162
Therefore, the area of trapezoid KLMN is 162 square units.