Answer: See explanation
Step-by-step explanation:
ΔLNM and ΔLKN are 30°- 60°- 90° triangles
We have to find the length of LN before we can find the length of MN.
In a 30°- 60°- 90° triangle, the length of the hypotenuse is 2 times the length of the shorter leg, and the length of the longer leg is the length of the shorter leg times √3
Since the hypotenuse is 6, the short leg would be 3 since the hypotenuse is 2 times the length of the short leg.
LN = √3 times the shorter leg
3 × √3 = 3√3
LN = 3√3
We now know the length of the longer leg in ΔLNM (3√3)
MN would be 3√3 × √3
3√3 × √3
= 3√9
= 3 × 3 = 9
MN = 9
ΔLKM is also a 30° - 60° - 90° triangle
The short leg is 6 m
The hypotenuse would be 12 m
The longer leg would be 6√3
Perimeter: 6 + 12 + 6√3
The perimeter is 18 + 6√3
Area: 1/2 × b × h
b = 6√3
h = LN = 3√3
6√3 × 3√3
18√9 = 18 × 3 = 54
Area: 54 m²
Hope it helps!!
