Question

Hey, can someone help me with Math assignment?

A right prism has a base in the shape of an octagon. The side length of the octagon is 4 inches. The length of the apothem is 4.83 inches. The height of the prism is 12 inches. What is the volume of the prism? Round your answer to the nearest whole number.


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Answer 1

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In ATTATCHMENT.............

Answer 2

Answer :

The Area of the prism = 927 inches²

Step-by-step explanation :

Given :

Length of the side of the octagon is 4 inches.

The length of the apothem is 4.83 inches.

Height of the prism is 12 inches.

Volume of the prism      ?

To Find :

The volume of the prism.

Solution :

We know that :

Area of the prism :

$\bigstar\;\boxed{\sf Area\;of\;the\;Base\timesHeight}}$

So,

It is Given,

Base of the prism is an octagon with side length = 4 inches  and apothem = 4.83 inches.

First of all,

To Find :

Area of the octagonal base.

We also know that :

Area of the octagonal base :

$\bigstar\;\dfrac{1}{2}(\text{Perimeter})(\text{Apothem})$

So,

$\sf \implies \dfrac{1}{2}(4)(8)(4.83)$

$\sf \implies 77.28\;Inch^2$

Now,

Area of the prism :

⇒ 12 × 77.28

⇒ 927.36 inch²

Therefore, area of the prism having base in the shape of an octagon is:

927 inch²

{ Rounded off Value As given in Question! }