Question

Calculate the area of triangle having length of its sides are 25 cm, 20 cm and 35 cm.​

Answer 1

Answer:

The area of triangle is 244.9 cm².

Step-by-step-explanation:

We have given that,

The lengths of sides of triangle are

• s₁ = 25 cm
• s₂ = 20 cm
• s₃ = 35 cm

We have to find the area of the triangle.

Now, we know that,

Semiperimeter of triangle = ( Sum of sides ) / 2

⇒ s = ( s₁ + s₂ + s₃ ) / 2

⇒ s = ( 25 + 20 + 35 ) / 2

⇒ s = ( 25 + 5 + 15 + 35 ) / 2

⇒ s = ( 30 + 50 ) / 2

⇒ s = 80 ÷ 2

⇒ s = 40 cm

∴ Semiperimeter of triangle = 40 cm

Now, by Heron's formula,

Area of triangle = √[ s ( s - s₁ ) ( s - s₂ ) ( s - s₃ ) ]

⇒ A = √[ 40 ( 40 - 25 ) ( 40 - 20 ) ( 40 - 35 ) ]

⇒ A = √( 40 * 15 * 20 * 5 )

⇒ A = √( 4 * 10 * 5 * 3 * 4 * 5 * 5 )

⇒ A = √( 4 * 5 * 2 * 5 * 3 * 4 * 5 * 5 )

⇒ A = √( 4 * 4 * 5 * 5 * 5 * 5 * 3 * 2 )

⇒ A = 4 * 5 * 5 * √( 3 * 2 )

⇒ A = 4 * 25 * √6

⇒ A = 100 √6

⇒ A = 100 * 2.449

⇒ A = 244.9 cm²

∴ The area of triangle is 244.9 cm².

Answer 2

Given :

Sides of triangle are

a = 25cm

b = 20cm

c = 35cm

To Find :

Area of the triangle

Solution :

semi perimeter (s) = (a + b + c)/2

= (25 + 20 + 35)/2

= (80)/2

s = 40cm

then by using Heron's Formula :-

Area = √s(s - a) (s - b) (s - c)

⇒ √40 (40 - 25) (40 - 20) (40 - 35)

⇒ √40 * 15 * 20 * 5

⇒ √60000

⇒ 244.94 cm²

⇒ 245cm² (approx.)

∴ Area of the Triangle is 245cm²