Question

Use the net to find the surface area of the regular pyramid. mm2

Answer 1

Answer:

$A_{S} = \frac{p_{b}}{2}\cdot (l_{b}+l)$

Step-by-step explanation:

The surface area of the regular pyramid is equal to the sum of the base and lateral areas:

$A_{S} = A_{b} + A_{l}$

Where the base area is equal to:

$A_{b} = \frac{p_{b}\cdot l_{b}}{2}$

In which $p_{b}$ and $l_{b}$ are the base perimeter and slant, respectively.

And the lateral area is:

$A_{l} = \frac{p_{b}\cdot l}{2}$

Where $l$ is the side slant.

By substituting and simplifying the expression, the formula of the surface area for a regular pyramid is found:

$A_{S} = \frac{p_{b}\cdot l_{b}}{2}+\frac{p_{b}\cdot l}{2}$

$A_{S} = \frac{p_{b}}{2}\cdot (l_{b}+l)$