Question

the side of triangle are 40 cm 70 cm 90 cm find the area of the triangle​

Answer 1

Answer:

600√5

By herons formula.....

Answer 2

Answer:

The area of the triangle is 600 √5 cm².

Step-by-step-explanation:

We have given the sides of a triangle.

We have to find the area of the triangle.

s₁ = 40 cm

s₂ = 70 cm

s₃ = 90 cm

Now, we know that,

Semi perimeter of triangle = ( Sum of sides ) / 2

⇒ s = ( s₁ + s₂ + s₃ ) / 2

⇒ s = ( 40 + 70 + 90 ) / 2

⇒ s = ( 40 + 60 + 10 + 90 ) / 2

⇒ s = ( 100 + 100 ) / 2

⇒ s = 200 ÷ 2

⇒ s = 100 cm

Now, by Heron's formula,

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

⇒ Area of triangle = √[ 100 ( 100 - 40 ) ( 100 - 70 ) ( 100 - 90 ) ]

⇒ Area of triangle = √( 100 * 60 * 30 * 10 )

⇒ Area of triangle = √( 10 * 10 * 4 * 15 * 10 * 3 * 10 )

⇒ Area of triangle = √( 10 * 10 * 4 * 3 * 5 * 10 * 10 * 3 )

⇒ Area of triangle = √( 10 * 10 * 2 * 2 * 3 * 3 * 10 * 10 * 5 )

⇒ Area of triangle = 10 * 2 * 3 * 10 √5

⇒ Area of triangle = 10 * 10 * 2 * 3 √5

⇒ Area of triangle = 100 * 6 √5

⇒ Area of triangle = 600 √5 cm²

∴ The area of the triangle is 600 √5 cm².