The problem involves an equilateral triangle, which is a triangle with all sides of equal length. The formula for the area of an equilateral triangle is given by √3/4 * a^2, where 'a' is the length of a side. However, the problem asks us to use Heron's formula.

Heron's formula for the area of a triangle with sides a, b, and c is given by √[s(s - a)(s - b)(s - c)], where s is the semi-perimeter of the triangle, calculated as (a + b + c) / 2.

In this case, since the triangle is equilateral, a = b = c. The perimeter of the triangle is given as 180 cm, so each side of the triangle (a) is 180 / 3 = 60 cm.

The semi-perimeter (s) of the triangle is therefore 180 / 2 = 90 cm.

Substituting these values into Heron's formula gives:

Area = √[90(90 - 60)(90 - 60)(90 - 60)]
= √[90 * 30 * 30 * 30]
= √[24300000]
= 4930.75 cm^2

So, the area of the signal board is 4930.75 cm^2.

Question

The problem involves an equilateral triangle, which is a triangle with all sides of equal length. The formula for the area of an equilateral triangle is given by √3/4 * a^2, where 'a' is the length of a side. However, the problem asks us to use Heron's formula.

Heron's formula for the area of a triangle with sides a, b, and c is given by √[s(s - a)(s - b)(s - c)], where s is the semi-perimeter of the triangle, calculated as (a + b + c) / 2.

In this case, since the triangle is equilateral, a = b = c. The perimeter of the triangle is given as 180 cm, so each side of the triangle (a) is 180 / 3 = 60 cm.

The semi-perimeter (s) of the triangle is therefore 180 / 2 = 90 cm.

Substituting these values into Heron's formula gives:

Area = √[90(90 - 60)(90 - 60)(90 - 60)]
     = √[90 * 30 * 30 * 30]
     = √[24300000]
     = 4930.75 cm^2

So, the area of the signal board is 4930.75 cm^2.

Knowee AI · Accepted Answer

The problem involves an equilateral triangle, which is a triangle with all sides of equal length. The formula for the area of an equilateral triangle is given by √3/4 * a^2, where 'a' is the length of a side. However, the problem asks us to use Heron's formula.

Heron's formula for the area of a triangle with sides a, b, and c is given by √[s(s - a)(s - b)(s - c)], where s is the semi-perimeter of the triangle, calculated as (a + b + c) / 2.

In this case, since the triangle is equilateral, a = b = c. The perimeter of the triangle is given as 180 cm, so each side of the triangle (a) is 180 / 3 = 60 cm.

The semi-perimeter (s) of the triangle is therefore 180 / 2 = 90 cm.

Substituting these values into Heron's formula gives:

Area = √[90(90 - 60)(90 - 60)(90 - 60)]
     = √[90 * 30 * 30 * 30]
     = √[24300000]
     = 4930.75 cm^2

So, the area of the signal board is 4930.75 cm^2.

A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle withside ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is180 cm, what will be the area of the signal board?

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