Question

the area of the rectangular face of a uniform triangular prism is 60 cm2 and the perimeter of the triangular faces is 18cm. what is the volume of prism in cm3 ?​

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  $=\frac{18}{3} cm$  $=6 cm$

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

∴ Height of the prism $= \frac{60}{6} cm = 10 cm$

∴ Volume of the prism  = Area of one Triangular face x Height of the prism

$=\sqrt{s(s - a)^3}$ x 10 $cm^3$

where s is half the perimeter of Triangular Side, and a is each side.

∴ Volume of the prism  $=\sqrt{9(9 - 6)^3} . 10 cm^3= 90\sqrt{3} cm^3$