Question

If the total area of the pyramid is 1276, what is the height of a triangle??

Answer 1

Answer:

18 cm

Step-by-step explanation:

The total surface area of a square pyramid is given by the formula:

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

Where:

• $A$ is the total surface area of the pyramid,
• $B$ is the area of the base (which is a square),
• $P$ is the perimeter of the base square,
• $l$ is the slant height of the pyramid.

Given that the total area of the square pyramid is $1276 \, \text{cm}^2$ and the side of the square base is $22 \, \text{cm}$, we can first find the perimeter of the base:

$\textsf{Perimeter} = 4 \times \textsf{Side} \\\\ = 4 \times 22 \\\\= 88 \, \textsf{cm}$

Now, using the formula for the total surface area and plugging in the values:

$1276 = 22^2 + \dfrac{1}{2} \times 88 \times l$

$1276 = 484 + 44l$

$44l = 1276 - 484$

$44l = 792$

$l = \dfrac{792}{44}$

$l = 18 \, \text{cm}$

So, the slant height of the square pyramid is $18 \, \text{cm}$.