If its Perimeter of an Equilateral Triangle is 180cm, What will be its Area?

If its Perimeter of an Equilateral Triangle is 180cm, What will be its Area?

To solve the problem of finding the area of an equilateral triangle given its perimeter as 180 cm, follow these steps.

Since an equilateral triangle has all sides equal, we divide the perimeter by 3 to get the length of one side:

180/3 = 60 cm.

The formula to calculate the area of an equilateral triangle is

√3/4 x a²

where a is the length of a side.

Substitute the length of one side, which is 60 cm, into the area formula:

√3/4 x 60² = 900√3 square centimeters

Thus the exact value of 900√3 which is approximately 1558.84 square centimeters.

Area of an Equilateral Triangle

An equilateral triangle is a type of triangle where all three sides are of equal length. This means that all three angles in the triangle are also equal, each measuring 60 degrees.

Calculating the Area of an Equilateral Triangle

The formula to find the area of an equilateral triangle is √3/4 x a²

where a is the length of one side

This formula is derived from the trigonometric properties of equilateral triangles.

Measure the length of one side of the equilateral triangle.

Substitute the side length into the area formula:

Area = √3/4 x a²

Perimeter and Area Relationship

The perimeter of an equilateral triangle is the sum of the lengths of all three sides.

Once the side length is known, put it into the area formula to find the exact area of the equilateral triangle.