Question

If the perimeter of an equilateral triangle is 30 ft, what is the area?

Answer 1

Divide the perimeter by 3 to find the side length.
Since the formula for the are of a triangle is
1/2 * b * h the height must be found.
If a perpendicular line is drawn from the apex of the triangle, a right triangle is formed with a base of 5 and a hypotenuse of 10. Also since it originally was equilateral the base angle is 60 degrees. The rules for finding lengths of sides of equal. Triangles is long leg = sqrt3 * short leg
the height is the long leg so the height is 5sqrt3.
A=(1/2)(10)(5sqrt3)= 25sqrt3