Question

Find the missing side using Pythagorean theorem, than find the surface area

Answer 1

Given:

Consider the triangular part in the given figure.

To find the third side of right triangle. Use pythagorean theorem,

$\begin{gathered} x^2=3^2+4^2 \\ x^2=9+16 \\ x^2=5^2 \\ x=5 \end{gathered}$

The missing side of triangle is 5 cm.

Now to find the surface area of triangular prism.

Note that the height of the right triangle is 4 cm and base is 3 cm.

$s_1=3,s_2=4,s_3=5,l=6,h=4,b=3$

First calculate the area of each side,

$\begin{gathered} \text{Area of one triangle=}\frac{1}{2}(4\times3)=6 \\ \text{Area of second triangle}=\frac{1}{2}(4\times3)=6 \\ \text{One rectangle =4}\times6=24 \\ \text{second rectangle}=3\times6=18 \\ \text{Third rectangle =}5\times6=30 \end{gathered}$

So, the surface area is,

$SA=6+6+24+18+30=84$

Answer: surface area is 84 square cm.