Question

A signboard is in the shape of an equilateral triangle with side 'a'. Find the area of the signboard using Heron's formula. If the perimeter of the board is 210 cm, what will be its area ?​

Answer 1

Given :-

A signboard is in the shape of an equilateral triangle with side 'a'. Find the area of the signboard using Heron's formula. If the perimeter of the board is 210 cm

To Find :-

Area using heron's formula

Solution :-

In an equilateral triangle

Perimeter = a + a + a

210 = a + a + a

210 = 3a

210/3 = a

70 = a

Therefore

Side are 70 cm, 70 cm and 70 cm

Now,

Semiperimeter = Perimeter/2

Semiperimeter = 210/2

Semiperimeter = 105 m

Area = √s(s - a)(s - b)(s - c)

Area = √105(105 - 70)(105 - 70)(105 - 70)

Area = √105 × 35 × 35 × 35

Area = √4501875 cm

Area = 2121.76 cm²

Hence

Area is 2121.76 cm²

Answer 2

Given :-

• Perimeter of signboard = 210cm

To Find :-

• The Area of Signboard = ?

Solution :-

To calculate the area of signboard at first we have to notice in the given question. As given in the question that A signboard is in the shape of an equilateral triangle with side 'a'. Find the area of the signboard using Heron's formula. If the perimeter of the board is 210 cm. At calculate it's sides by applying formula then calculate it area by applying herons formula.

Calculation begins :-

⟹ Perimeter of signboard = 3 × a

⟹ 3a = 210

⟹ a = 70cm

Now calculate Area of Signboard :-

⟹ S = a + b + c/2

• a = b = c ( in eq ∆ sides are eq)

⟹ S = 70 + 70 + 70/2

⟹ S = 210/2

⟹ S = 105cm

By Applying herons formula we get :-

⟹ Area of Signboard = √s(s - a)(s - b)(s - c)

⟹ A = √105(105 - 70)(105 - 70)(105 - 70)

⟹ A = √105 × 35 × 35 × 35

⟹ A = √ 35 × 3 × 35 × 35 × 35

⟹ A = 35 × 35 × √3

⟹ A = 1225√3 cm²

Hence,

• The area of signboard = 1225√3 cm²