SOLUTION: 37) Find the area of an equilateral triangle with apothem 9.

Question 973425: 37) Find the area of an equilateral triangle with apothem 9.
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
s=side of equilateral triangle, a=apothem=9
The apothem is the longer leg of a 30-60-90 triangle
with one side of the equilateral triangle as hypotenuse
and one half one side as the shorter leg.

Multiply by 4

The side of the equilateral triangle is 10.39.
The base of the right triangle which makes up half of the
equilateral triangle is 1/2 of a side (1/2)(10.39)=5.195 units
The height of this right triangle is the apothem (9 units)
The area of the right triangle is (1/2)(5.195)(9)=23.4 square units
Since two of these right triangles make up the equilateral triangle,
area of the equilateral triangle is (2)(23.4)=46.8 square units.

RELATED QUESTIONS
find the area of an equilateral triangle with apothem of 11 cm Thank... (answered by greenestamps,Istar31)

an equilateral triangle with apothem 2, what is the... (answered by Alan3354)

Find the area of an equilateral triangle, with apothem 10 times the square root of 3.... (answered by solver91311)

Find the area of an equilateral triangle (regular 3-gon) with the given measurement if... (answered by Fombitz)

Find the area of an equilateral triangle (regular 3-gon) with the given measurement.... (answered by edjones)

What is the area of an equilateral triangle with apothem... (answered by RAY100)

find the area of an equilateral triangle with an apothem having a length of 4 feet. round (answered by solver91311)

what is the area of an equilateral triangle (regular 3-gon) with the given measurement (answered by CharlesG2)

what is the area of an equilateral triangle whose apothem is 8... (answered by Theo)