Question

The base of a prism is a right angled triangle having its base and altitude as 12 cm and 16 cm respectively. What is the total surface area of the prism if height of prism is 22 cm?

• A. $1296c{m}^2$
  
• B. $1148c{m}^2$
  
• C. $1248c{m}^2$
  
• D. $1295c{m}^2$

Answer 1

The correct option is C

$1248c{m}^2$

Base of the prism is a right-angled triangle having its base and altitude as 12 cm and 16 cm respectively.

Hence, the third side will be equal to

$\sqrt{{12}^2+{16}^2}=\sqrt{144+256}=\sqrt{400}=20cm$

Total area = Lateral surface area + Area of 2 triangles (base and top)

Total area

$=12\times 22+16\times 22+20\times 22+2\times \frac{1}{2}\times 12\times 16$

$=22(12+16+20)+12\times 16$

$=1056+192$

$=1248c{m}^2$