Question

the base of a Prism is triangular in shape with sides 3 cm 5 cm and 4 cm find the volume of the prism if its height is 10 cm

Answer 1

Volume of prism =area of base*height
volume of prism = 6cm² * 10 cm
volume of prism =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 .