Question

The base of a prism is a right angled triangle with dimensions as follows:
Base = 15 cm
Altitude = 8 cm
If the height of the prism is 20 cm, find the total surface area of the prism.

Answer 1

Base of the prism is a right angled triangle having base and altitude as 15 cm and 8 cm, respectively.
Third side of the triangle will be equal to:

$\sqrt{(15{)}^2+(8{)}^2}=\sqrt{225+64}=\sqrt{289}=17\text{cm}$

Total surface area = Lateral surface area + $2\times BaseArea$

Lateral Surface Area =$BasePerimeter\times Height$
= $20(15+8+17)$ $c{m}^2$

$=20(15+8+17)+2\times \frac{1}{2}\times 15\times 8$

$=20(15+8+17)+15\times 8$

$=20\times 40+120$

$=800+120$

$=920{\text{cm}}^2$

Total Surface Area $=920{\text{cm}}^2$