lateral surface area of pentagonal prism; base-edge lengths, height of right prism;

kidwizard

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Could you please guide me and help me with these problems?

1. The lateral surface area of a regular pentagonal prism is 360 square feet. The height of the prism is twice the length of one of the edges of the base. Find the surface area of the prism. Round your answer to the nearest hundredth.

2. Describe how multiplying the base-edge lengths by 1/4 and the height by 4 affects the surface area of the right prism.

help2.jpg

3. A right cylinder has a surface area of \(\displaystyle 108\pi\) square meters. The radius of the cylinder is twice the height. Write and solve an equation to find the height "h" in meters of the cylinder.

help3.jpg
 
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Could you please guide me and help me with these problems:


1.The lateral surface area of a regular pentagonal prism is 360 square feet. The height of the prism is twice the length of one of the edges of the base. Find the surface area of the prism. Round your answer to the nearest hundredth.



.
View attachment 9402View attachment 9403
View attachment 9402View attachment 9403

What are your thoughts?

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Could you please guide me and help me with these problems:


1.The lateral surface area of a regular pentagonal prism is 360 square feet. The height of the prism is twice the length of one of the edges of the base. Find the surface area of the prism. Round your answer to the nearest hundredth.



.
View attachment 9402View attachment 9403

The picture seems to be for another problem.

What formula do you know for the lateral surface area of a prism? That should give you an equation relating the height and the length of each edge of the base. Use the second sentence to turn this into a single equation in a single variable.

Please show us what you know, and what you are able to do, so we can help you get beyond that.
 
1. The lateral surface area of a regular pentagonal prism is 360 square feet. The height of the prism is twice the length of one of the edges of the base. Find the surface area of the prism.
What is meant by "lateral" surface area? How many lateral sides does this shape have? If the length of one edge of the base is "b", then what expression stands for the height? Where does this lead?

2. Describe how multiplying the base-edge lengths by 1/4 and the height by 4 affects the surface area of the right prism.

View attachment 9402
The image is tiny and a bit blurry, so I'm not sure: Is the triangle (forming the top and the bottom) a right triangle? (The "right" in "right prism" just means that the sides are vertical, rather than angled at all.)

3. A right cylinder has a surface area of \(\displaystyle 108\pi\) square meters. The radius of the cylinder is twice the height. Write and solve an equation to find the height "h" in meters of the cylinder.

View attachment 9403
What is the formula for the surface area A of a right (circular?) cylinder with radius r and height h? If "h" stands for the height, then what expression stands for the radius? Plugging this and the given information into the known formula, what do you get? Where does this lead?

Please be complete. Thank you! ;)
 
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