Question

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 1

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 .

Answer 2

Given :-

• The Base of a prism is in triangular shape
• Sides of the base given as 3 cm, 4 cm and 5 cm respectively.
• Prism height = 10 cm.

To Find :-

• Find the volume of the prism.

Solution :-

As we know ,

• Volume of prism = Area of base × Height .

Height is already given as 10 cm

we need to find area first

For area, we need to know the sides , which is also given as :-

• a = 3 cm
• b = 4 cm
• c = 5 cm

By using heron's formula :-

Finding the " s " { semi perimeter } first

Semi perimeter = ( a + b + c ) / 2

➨ S = (a + b + c) / 2

Substituting the values , we get :

➨ (3 + 4 + 5) / 2

➨ 12 / 2

➟ S = 6 cm

We got ' s ' now , is 6 cm.

Applying heron's formula :

Area of Triangle = √s(s - a) (s - b) (s - c)

➨ √6(6 - 3) (6 - 4) (6 - 5)

➨ √6 × 3 × 2 × 1

➨ √36

➟ Area = 6 cm²

Therefore,

Area of base is 6 cm²$.$

Now, Using the formula for volume of prism :-

Volume of prism = Area of base × Height of prism

Putting Values in the above formula , we get :-

➨ V = 6 × 10

➟ V = 60 cm³

So,

The volume of prism = 60 cm³ .

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