What is the area of an equilateral triangle with perimeter of 36 inches?

Question

(A) 144 sq. in.

(B) 72 sq. in.

(C) 81 sq. in.

(D) 324 sq. in.

(E) None of the above

I got (E) None of the above, is this correct?

Answer 1

That is correct.

Explanation: An equilateral triangle has 3 sides of the same length and the perimeter is given as 36, therefore each side is 12 inches. The formula for the area of a triangle is base*height/2. We know the base is 12 because each side is 12. To find the height, draw the triangle with a line in the middle to represent the height. You'll notice it forms a right triangle, therefore we can use the Pythagorean theorem: a²+b²=c² to solve for the height. Use these values in the area formula and you will get a value that is not choice A, B, C or D.