the perimeter of an equilateral triangle is 24 ft. Find it's exact area.

Question

the answer should not have a simplified radical.  

Answer 1

Thank you for the correction, Mark M.

All three sides of the triangle are equal, so 24/3 = 8 ft = length of each side

 

The formula for the area of a triangle is listed below, where b = base and h = height:

 

The height of the triangle will divide the bottom in half and will form two right-triangles of equal dimensions. The hypotenuse of each right triangle will be 8, and one leg will be 4. The height of the equilateral triangle will represent the other leg of the triangle, and its length is unknown, so we will call it x. We can use the Pythagorean Theorem to compute its length. a² + b² = c², where c = the hypotenuse 4² + b² = 8² 16 + b² = 64 b² = 48 b = 4√3 = the height of the equilateral triangle Now that we have the height, we can compute the area of the equilateral triangle. A = (1/2)(8)(4√3) = 4(4√3) = 16√3 ft²