An equilateral triangle has a perimeter of 120 inches. What is the area of the triangle? Express your answer in simplest radical form.

To find the area of an equilateral triangle, we need to know the length of one of its sides. Given that the triangle has a perimeter of 120 inches, we can divide this by 3 since all sides of an equilateral triangle are equal.

120 inches ÷ 3 = 40 inches

So, each side of the equilateral triangle is 40 inches long.

To find the area of an equilateral triangle, we can use the formula:

Area = (√3/4) × a^2

Where "a" is the length of one side of the triangle.

Plugging in the value of "a" as 40 inches, we have:

Area = (√3/4) × (40 inches)^2

Area = (√3/4) × 1600 square inches

To simplify the square root, we have (√3/4) × 1600 = (√3 × 1600) / 4 = (40√3) / 4

Simplifying further, we get (40/4) × √3 = 10 × √3

So, the area of the equilateral triangle is 10√3 square inches.

To find the area of an equilateral triangle, we need to know the length of the sides. From the problem, we are given the perimeter of the triangle, which is 120 inches.

Since an equilateral triangle has all sides equal, we can divide the total perimeter by the number of sides to find the length of each side.

Perimeter = Sum of all side lengths

120 inches = 3 * (Length of each side)

Dividing both sides of the equation by 3, we get:

Length of each side = 120 inches / 3 = 40 inches

Now that we know the length of each side, we can use the formula for the area of an equilateral triangle:

Area = (sqrt(3)/4) * (Length of each side)^2

Substituting the values we found:

Area = (sqrt(3)/4) * (40 inches)^2

Area = (sqrt(3)/4) * (1600 square inches)

Now we simplify the expression:

Area = (sqrt(3)/4) * 1600 square inches

To express the answer in simplest radical form, we can simplify the square root of 1600:

The square root of 1600 = 40

Therefore, the area of the equilateral triangle is:

Area = (sqrt(3)/4) * 40 * 40 square inches

Area = (sqrt(3)/4) * 1600 square inches

Area = 400 * (sqrt(3)/4) square inches

Area = 100 * (sqrt(3)) square inches

So, the area of the equilateral triangle is 100 * (sqrt(3)) square inches.

each side is 40

area = (1/2)(40)(40)sin60 = 800√3/2 = 400√3

Whenever you see equilateral, just remember that it means all sides are equal. (tip: equil->equal, same pronounciation)