Question

The area of the rectangular face of a uniform triangular prism is 60 cm2 and the perimeter of the triangular faces is 18 cm. What is the volume of the prism in cm​

Answer 1

Answer:

Volume of the prism $= 90\sqrt{3}$ $cm^3$

Step-by-step explanation:

The area of the rectangular face of a uniform triangular prism is $60 cm^2$

And the perimeter of the triangular faces is $18 cm$

∴ Sum of the uniform sides of triangular face $=18 cm$

=> 3 times each of the sides of triangular face $=18 cm$

∴ Each of the sides of triangular face $= \frac{18}{3} = 6 cm$

Now the area of the rectangular face = side of the triangular face x height of the prism.

∴ Height of the prism $= \frac{Area of the rectangular face }{Side of the triangular face}$ $= \frac{60}{6} = 10 cm$

∴ Volume of the prism $= (Area of one Triangular Side) . (Height of the Prism)$

$= (\sqrt{s(s - a)^3}) . Height of the prism$ where s is half the perimeter of Triangular Side, and a is each side.

$= (\sqrt{9(9 - 6)^3}) . (10)$ $= 90\sqrt{3}$ $cm^3$