Question

What's the formula of prisms?

Question: Find the TOTAL surface area of this square-based pyramid.

SA=

Answer 1

Answer:

$\sf SA = 125 \, \textsf{in}^2$

Step-by-step explanation:

The total surface area ($A$) of a square-based pyramid can be calculated using the formula:

$\Large\boxed{\boxed{\sf SA = B + \dfrac{1}{2}Pl}}$

where

• $\sf B$ is the area of the base,
• $\sf P$ is the perimeter of the base, and
• $\sf l$ is the slant height.

For a square base, the area of the base ($B$) is the side length squared ($s^2$).

Given that the base side length ($s$) is 5 in and the slant height ($l$) is 10 in:

Calculate the area of the base ($B$):

$\sf B = s^2 \\\\ = 5^2 \\\\= 25 \, \textsf{in}^2$

Calculate the perimeter of the base ($P$) for a square:

$\sf P = 4s\\\\ = 4 \times 5 \\\\= 20 \, \textsf{in}$

Substitute the values into the formula for the total surface area ($A$):

$\sf SA = B + \dfrac{1}{2}Pl$

$\sf SA = 25 + \dfrac{1}{2} \times 20 \times 10$

$\sf SA = 25 + 100$

$\sf SA = 125 \, \textsf{in}^2$

So, the total surface area of the square-based pyramid is:. $125 \, \textsf{in}^2$