Question

SKILL
Given that one side of an equilateral triangle is 16, what is the area of the triangle?

Answer 1

approximately 55.43 or
`4√(192)`

Explanation:

1) draw line down middle of said triangle and split it in half

2) since the area of the triangle is 1/2 b * h we can solve

3) we know that the base is 8 (16 split in 1/2)

4) use the Pythagorean theorem (a^2 +b^2 = c^2) to solve for the height

5) a= 8 b= ? c= 16

6) 16^2=256 8^2= 64 256-64=b^2

7) b=
`√(192)`

8)
`(1)/(2) *√(192) *8= 4√(192)` or approximately 55.43

You can check by substituting the numbers back into the Pythagorean theorem and see if they match up