Question

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

9-inch perimeter

Answer 1

An equilateral triangle with a 9-inch perimeter has sides of length 3. To find the area, we will want to find the height, so that we can use the familiar formula \(A=\frac 1 2 bh.\) So, we can draw an altitude which will bisect the base into two segments of length \(3/2.\) This will give us two identical right triangles, with hypotenuse 3 and one leg of length \(3/2.\) We can use the Pythagorean formula to solve for the altitude: \((3/2)^2+h^2=3^2.\) When we solve this equation, we will obtain \(h=\dfrac{3\sqrt3}2.\) We then solve for the area, and obtain \(A=\dfrac{9\sqrt3}4.\)