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# Help Zone

### Student Question

Secondary III • 5mo.

Is this correct? I don't know how to do it.

Mathematics

## Explanations (1)

• Explanation from Alloprof

Explanation from Alloprof

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Team Alloprof • 5mo.

Hello NaiveGiganotosaurus556,

Please come back with more details of the problem or a better drawing, because it is unclear. From the looks of it, you have a hexagonal pyramid attached to a prism that is sitting on a circle. Shouldn't it be a hexagon?

The lateral area of a pyramid is given by

$$A_L = \dfrac{P_b \times a}{2}$$

where

\begin{align}A_L&=\text{Lateral area}\\P_b&=\text{Base perimeter}\\a &= \text{Pyramid apothem}\end{align}

The lateral area of a prism is calculated with

$$A_L = P_b \times h$$

where

\begin{align} A_L&=\text{Lateral area} \\ P_b &= \text{Perimeter of a base}\\ h\ &= \text{Prism height}\end{align}

If the base is a hexagon, it is the same as the base of the hexagonal pyramid.

\begin{align} A_b &=A_{\text{regular polygons}}\\&= \dfrac{s \times a\times n}{2}\\ \end{align}

If it is a circle, then you are right to use πr², but be careful because there is only one not two.

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