Question

The bade if a prism is a regular pentagon with sides 5 feet long and an apothem of 3.4 feet. If the prism us 6 feet tall, what is the volume of the prism?

Answer 1

The bade if a prism is a regular pentagon with sides 5 feet long and an apothem of 3.4 feet. If the prism us 6 feet tall, what is the volume of the prism?

Solution:

The volume of the prism is

$$V = \text{AreaABCDE} * H$$ $$\text{AreaABCDE} = 5 \text{Area} \Delta AOB$$ $$\text{Area} \Delta AOB = \frac{AB * OM}{2}$$

Given:

$$AB = 5 \text{ feet}$$ $$OM = 3.4 \text{ feet}$$ $$H = 6 \text{ feet}$$

So

$$V = 5 * \frac{5 * 3.4}{2} * 6 = 153 \text{ cubic feet}$$

Answer: The volume of the prism is 153 cubic feet