Given: KLMN is a trapezoid, m∠K = 90°, LM = 9, KN = 18, MN = 15 Find: Area of KLMN
LM and KN are parallel
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.
KN =KS +SNKS =10Δ MSN is isosceles, because m∠MSN=90⁰, m∠N=45⁰, so m∠NMS=45⁰,
and MS=SN=10.KN =KS +SN =10+10=20
KN=20Area of a trapezoid = (1/2)*(b1+b2)*h
b1=10, b2=20, h=10Area of a trapezoid = (1/2)*(10+20)*10=150Area of trapezoid KLMN =150KN=20
To find the area of trapezoid KLMN, we can use the formula:
Area = (1/2) * (sum of the lengths of the parallel sides) * (perpendicular distance between the parallel sides)
In this case, the parallel sides are LM and KN.
Given:
LM = 9
KN = 18
MN = 15
First, we need to find the perpendicular distance between the parallel sides (LM and KN). To do this, we can use the Pythagorean theorem.
Since angle K is a right angle (m∠K = 90°), we can use the length of MN as the height (perpendicular distance) between LM and KN.
Using the Pythagorean theorem, we can calculate the height (h) as:
h^2 = KN^2 - MN^2
h^2 = 18^2 - 15^2
h^2 = 324 - 225
h^2 = 99
h ≈ √99
h ≈ 9.95
Now, we have all the values we need to calculate the area of trapezoid KLMN.
Area = (1/2) * (LM + KN) * h
Area = (1/2) * (9 + 18) * 9.95
Area = (1/2) * 27 * 9.95
Area ≈ 13.5 * 9.95
Area ≈ 134.325
Therefore, the area of trapezoid KLMN is approximately 134.325 square units.
No, but the answer is not twelve for this, so can you please solve it
looks like the same problem here:
http://www.jiskha.com/display.cgi?id=1493855490