Question

The base of a prism is in the shape of equilateral triangle.Its base perimeter is 6 cm and height 5cm.Find the volume.​

Answer 1

Answer:

• The volume of Prism is approx 8.66 cm³.

Step-by-step explanation:

Given:-

• Base of a prism is in the shape of equilateral triangle.

• Perimeter of triangular base = 6 cm.

• Height = 5 cm.

To Find:-

• It's Volume

Formula used:-

• Volume of Prism $=b×h$ where b = area of base

• Perimeter of equilateral triangle = 3a

• Area of Equilateral Triangle = $\dfrac{\sqrt{3}}{4}a²$

Solution:-

Firstly,

Perimeter of base of prism = 3a

• 6 = 3a

• a = 2 cm

Now,

Area of Equilateral Triangle = $\dfrac{\sqrt{3}}{4}a²$

Area = $\dfrac{\sqrt{3}}{4}×2²$

Area = $\dfrac{\sqrt{3}}{4}×4$

Area = $\sqrt{3}cm²$

Finally,

Volume of Prism $=b×h$

Volume of Prism $=5×\sqrt{3}$

Volume of Prism $=5\sqrt{3}$

Volume of Prism $=8.66 cm³$

Hence, the volume of given prism is approx 8.66 cm³.

━━━━━━━━━━━━━━━━━━

Answer 2

Step-by-step explanation:

Firstly,

Perimeter of base of prism = 3a

6 = 3a

a = 2 cm

Now,

Area of Equilateral Triangle = \dfrac{\sqrt{3}}{4}a²43a²

Area = \dfrac{\sqrt{3}}{4}×2²43×2²

Area = \dfrac{\sqrt{3}}{4}×443×4

Area = \sqrt{3}cm²3cm²

Finally,

Volume of Prism =b×h=b×h

Volume of Prism =5×\sqrt{3}=5×3

Volume of Prism =5\sqrt{3}=53

Volume of Prism =8.66 cm³=8.66cm³