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The answer is 162 square units. I got it right and I am in RSM. You can do this by:
1) You can find that KH is 9 because there is a rectangle.
2)You know that HN is 9 because KN = 18, and if KH is 9, then HN is 9. 18-9 = 9
3)Use Pythagorean theorem to find the hight of the triangle.
4)9^2 = 81, 15^2= 225, so 225-81=144, and the root of 144 is 12.
5) Now you know the height, so you can find the area of the rectangle.
6) 9*12 = 108 square units for the rectangle.
7) Find the area of the triangle. (9*12)÷2. 108÷2 = 54.
8) 54+108 = 162 square units.
1) You can find that KH is 9 because there is a rectangle.
2)You know that HN is 9 because KN = 18, and if KH is 9, then HN is 9. 18-9 = 9
3)Use Pythagorean theorem to find the hight of the triangle.
4)9^2 = 81, 15^2= 225, so 225-81=144, and the root of 144 is 12.
5) Now you know the height, so you can find the area of the rectangle.
6) 9*12 = 108 square units for the rectangle.
7) Find the area of the triangle. (9*12)÷2. 108÷2 = 54.
8) 54+108 = 162 square units.
The area of KLMN is 162 square units.
It is given that KLMN is a trapezoid, m∠K = 90° LM = 9, KN = 18, MN = 15, MH - altitude.
It is required to find the Area of KLMN.
What is a trapezoid?
It is defined as the quadrilateral having four sides in which two sides are parallel to each other it is a 2-dimensional geometry.
We have trapezoid KLMN in which
m∠K = 90°
LM = KH = 9
KN = 18
MN = 15 and
MH is the altitude.
Area of rectangle = length ×width
Area of rectangle = LM×MH
HN = KN - KH ⇒ 18 - 9 ⇒ 9
MH = [tex]\sqrt{MN^2-HN^2}[/tex] (from the Pythagoras theorem)
MH = [tex]\sqrt{15^2-9^2}[/tex]
MH = 12
Area of rectangle = LM×MH ⇒ 9×12 ⇒ 108
Area of triangle = [tex]\frac{HN\times MH}{2}[/tex] ⇒ [tex]\frac{9\times 12}{2} \Rightarrow 54[/tex]
Area of trapezoid = 108+54 ⇒ 162 square units.
Thus, the area of KLMN is 162 square units.
Learn more about the trapezoid here:
brainly.com/question/8643562
