Question

Two identical prisms with triangles as base are joined to form a rectangular prism as shown below.

What is the volume of the rectangular prism?

• A. 800 $c{m}^3$
• B. 900 $c{m}^3$
• C. 500 $c{m}^3$
• D. 1000 $c{m}^3$

Answer 1

The correct option is B 900 $c{m}^3$

Since the dimensions of the base triangle follow Pythagoras theorem i.e., ${13}^2=5^2+{12}^2$ we can conclude it is a right-angled triangle.

Hence, area of the triangular base

= $\frac{1}{2}\times 5\times 12$ = 30 $c{m}^2$

Volume of the triangular prism

= base area $\times$ height

= 30 $\times$ 15 = 450 $c{m}^3$

Now, the volume of the rectangular prism

= 2 $\times$ Volume of triangular prism

= 2 $\times$450

= 900 $c{m}^3$