What is the area of an equilateral triangle with an apothem of 6?

Answer 1

6 / √ 3 = x√ (3) / √ 3

Use the 30-60-90 rules

√ 3 would cancel out

2

6 / √ 3 (√ 3 / √ 3)

Cancel out √ 3 by multiplying the numerator and denominator by √ 3. You now will have :

6√ 3 / 3

3

6√ 3 / 3 = 2√ 3

Divide 6√ 3 by 3. You now have the base of the right triangle.

4

2√ (3) * 2 = 4√ 3

Multiply 2√ 3 by 2 to get the base of the equilateral triangle as well as all the sides.

5

4√ 3 * 6 = 24√ 3

24√3 / 2 = 12√ 3

Use the formula of A=BH/2 to find the final area of the triangle.