Question

The base of a rectangular prism, whose sides have lengths of 3 cm and 4 cm, is split vertically along its diagonal. If the height of the prism is 10 cm, then find the lateral surface area of each of these triangular prisms.

• A. $240c{m}^2$
• B. $60c{m}^2$
• C. $300c{m}^2$
• D. $120c{m}^2$

Answer 1

The correct option is D $120c{m}^2$

The base of the prism has sides whose lengths are 3 cm and 4 cm.

Diagonal of the base $=\sqrt{(3{)}^2+4^2}=\sqrt{25}=5cm$

Now, the splitting of the prism vertically along the diagonal of the base is shown below.

The blue colored plane splits the prism into 2 triangular prisms as shown below.

$\therefore$ Lateral surface area of the triangular prism $=3\times 10+4\times 10+5\times 10$
$=30+40+50$
$=120c{m}^2$