Question

The base of a prism is a rectangle with sides 3 cm and 4 cm respectively. The height of the prism is 10 cm. It is split vertically along a diagonal of the base into two triangular prisms. What is the total surface area of each of these triangular prisms?

• A. 100 $c{m}^2$
• B. 120 $c{m}^2$
• C. 130 $c{m}^2$
• D. 132$c{m}^2$

Answer 1

The correct option is D

132$c{m}^2$

Given: length of the rectangular base = 4 cm & breadth of the rectangular base = 3 cm

Since it is split along the diagonal: the third side of the triangle formed = $\sqrt{3^2+4^2}=5$

Height of the prism = 10 cm

Base Area of each triangular prism = $\frac{1}{2}\times 3\times 4$ = 6 $c{m}^2$

Lateral Surface Area = $BasePerimetre\times Height$ = $(3+4+5)\times 10$ = 120 $c{m}^2$

Total Surface Area of each Prism formed = Lateral Surface Area + $2\times BaseArea$

=120+ $2\times 6$ = 120+ 12

= 132 $c{m}^2$

Hence the total surface area of each triangular prism = 132 $c{m}^2$