Question

The base of a prism is a right angled triangle with dimensions as follows: base =15 cm and altitude= 8 cm. If the height of the prism is 20 cm, the total surface area of the prism will be equal to:

• A. $860{\text{cm}}^2$
• B. $820{\text{cm}}^2$
• C. $920{\text{cm}}^2$
• D. $960{\text{cm}}^2$

Answer 1

The correct option is C

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

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

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

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

$=20\times 40+120$

$=800+120$

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

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