Question

What will be the total surface area and lateral surface area of the prism formed on folding this net?

• A. Total Surface Area $=121$ cm${}^2$
  Lateral Surface Area $=173.5$ cm${}^2$
• B. Total Surface Area $=121$ cm${}^2$
  Lateral Surface Area $=133.5$ cm${}^2$
• C. Total Surface Area $=173.5$ cm${}^2$
  Lateral Surface Area $=121$ cm${}^2$
• D. Total Surface Area $=131$ cm${}^2$
  Lateral Surface Area $=173.5$ cm${}^2$

Answer 1

The correct option is C Total Surface Area $=173.5$ cm${}^2$

Lateral Surface Area $=121$ cm${}^2$
On folding this net, we will get a rectangluar prism with:
Length $l=7.5$ cm, Breadth $=5.5$ cm and Height $=3.5$ cm


For the lateral surface area, we have to find the area of the $4$ sides:


$\therefore$ Lateral Surface Area $=2\times (l\times b)+2\times (b\times h)$
$=2\times (7.5\times 5.5)+2\times (5.5\times 3.5)$
$=2\times \left(41.25\right)+2\times \left(19.25\right)$
$=82.5+38.5$
$=121$ cm ${}^2$

For the total surface area all $6$ sideas are taken into consideration.
$\therefore$ Total Surface Area $=$ Lateral Surface Area $+$ area of floor and ceiling
$=121+2\times (7.5\times 3.5)$
$=121+2\times \left(26.25\right)$
$=121+52.5=173.5$ cm${}^2$

Thus, Total Surface Area $=173.5$ cm${}^2$ and Lateral Surface Area $=121$ cm${}^2$

Option (c.) is correct.