1.

The Base of a prism is triangular in shape with sides 3 cm,4 cm,5 cm.Find the Volume of the prism of its Height is 10 cm.​

Answer»

A N S W E R :

  • Volume of prism is 60 cm³.

Given :

  • The Base of a prism is triangular in shape with sides 3 cm,4 cm,5 cm.
  • Height of prism is 10 cm.

To FIND :

  • The volume of prism = ?

Solution :

Let, sides of traingle be as :

  • a = 3 cm
  • b = 4 cm
  • c = 5 cm

Let's find the semi perimeter of traingle :

→ Semi perimeter = Sum of all sides of ∆ ÷ 2

→ Semi perimeter = (a + b + c) ÷ 2

→ Semi perimeter = (3 + 4 + 5) ÷ 2

→ Semi perimeter = 12 ÷ 2

→ Semi perimeter = 6 cm

  • Therefore,semi perimeter of traingle is 6 cm.

Now,calculate the AREA of a traingular base by HERON's formula :

⇒ Area of ∆ = √s(s - a) (s - b) (s - c)

⇒ Area of ∆ = √6(6 - 3) (6 - 4) (6 - 5)

⇒ Area of ∆ = √6 × 3 × 2 × 1

⇒ Area of ∆ = √36

⇒ Area of ∆ = 6 cm²

  • Hence,the area of traingular base is 6 cm².

Finding the volume of prism :

➻ Volume of prism = Area of traingular base × Height of prism

➻ Volume of prism = 6 × 10

➻ Volume of prism = 60 cm³

  • Hence,the volume of prism is 60 cm³ .


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