Question

Explain

Area of a Triangle - by Heron's Formula

Application of Heron's Formula in finding Areas of Quadrilaterals​

Answer 1

Answer :-

Area of a triangle by Heron's Formula:

Heron's formula was given by Heron, a mathematician in Alexandria in Egypt.

Area of triangle:

⟹ $\bold{\sqrt{s(s-a)(s-b)(s-c)} }$

Where:

• s = semi perimeter
• a = first side of the triangle
• b = second side of the triangle
• c = third side of the triangle

Why it is used:

Sometimes, when we are asked to find the area of a triangle, we can't find it's height, as the sides will be given, then this formula can only be used.

Example:

Find the area of the triangle with sides 6cm, 8cm and 10cm.

We have:-

a = 6 cm

b = 8 cm

c = 10 cm

Using Heron's formula:

• $\bold{\sqrt{s(s-a)(s-b)(s-c)} }$

Hence:-

We can find semi-perimeter with a, b, c.

⟹ a + b + c/2

⟹ 6 + 8 + 10/2

⟹ 24/2

⟹ 12 is the semi perimeter (s)

So:-

⟹ $\bold{\sqrt{s(s-a)(s-b)(s-c)} }$

⟹ $\bold{\sqrt{12(12-6)(12-8)(12-10)} }$

⟹ $\bold{\sqrt{12(6)(4)(2)} }$

⟹ $\bold{\sqrt{ 48\times12}=\sqrt{576}}$

⟹ 24 cm²

∴ The area of the triangle is 24 cm².

Answer 2

Answer:

Answer :-

Area of a triangle by Heron's Formula:

Heron's formula was given by Heron, a mathematician in Alexandria in Egypt.

Area of triangle:

⟹

$\bold{\sqrt{s(s-a)(s-b)(s-c)} }$

s = semi perimeter

a = first side of the triangle

b = second side of the triangle

c = third side of the triangle

Why it is used:

Sometimes, when we are asked to find the area of a triangle, we can't find it's height, as the sides will be given, then this formula can only be used.

Example:

Find the area of the triangle with sides 6cm, 8cm and 10cm.

We have:-

a = 6 cm

b = 8 cm

c = 10 cm

Using Heron's formula:

$</p><p>\bold{\sqrt{s(s-a)(s-b)(s-c)} }$

Hence:-

We can find semi-perimeter with a, b, c.

⟹ a + b + c/2

⟹ 6 + 8 + 10/2

⟹ 24/2

⟹ 12 is the semi perimeter (s)

So:-

⟹

$\bold{\sqrt{s(s-a)(s-b)(s-c)} }</p><p>⟹ \bold{\sqrt{12(12-6)(12-8)(12-10)} }</p><p>⟹ \bold{\sqrt{12(6)(4)(2)} }</p><p>⟹ \bold{\sqrt{ 48\times12}=\sqrt{576}}$

⟹ 24 cm²

∴ The area of the triangle is 24 cm².