Solve Precalculus Problem: Perimeter & Area of a Pentagon

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In summary, the formula for finding the perimeter of a pentagon is P = 5s, and the formula for finding the area is A = (1/4)√(5(5+2√5))s^2 or dividing it into 5 triangles and using A = (1/2)bh for each triangle. The Pythagorean Theorem cannot be used to solve for the sides of a pentagon. Perimeter is the distance around the outside of a shape, while area is the measure of the space inside a shape. It is possible for the perimeter of a pentagon to be greater than its area.
  • #1
pasatom20
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HI guys, I'm really confusing about this Q., and I hope you guys can give me some help. :smile:

- Find the perimeter and the area of a regular pentagon inscribed in circle of radius 9.
 
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  • #2
Break the inscribed pentagon into something simpler, such as triangles.
 
  • #3
Draw lines from the center of the circle to the vertices of the pentagon. What is the angle between these lines?
 
  • #4
I just figured out how to work on the problem. thanks everyone for helping me.
 

Related to Solve Precalculus Problem: Perimeter & Area of a Pentagon

1. What is the formula for finding the perimeter of a pentagon?

The formula for finding the perimeter of a pentagon is P = 5s, where P is the perimeter and s is the length of one side of the pentagon.

2. How do I find the area of a pentagon?

To find the area of a pentagon, you can use the formula A = (1/4)√(5(5+2√5))s^2, where A is the area and s is the length of one side of the pentagon. Alternatively, you can divide the pentagon into 5 triangles and use the formula A = (1/2)bh for each triangle, then add the areas together.

3. Can I use the Pythagorean Theorem to solve for the sides of a pentagon?

No, the Pythagorean Theorem only applies to right triangles. A pentagon is not a right triangle, so the Pythagorean Theorem cannot be used to solve for its sides.

4. What is the difference between perimeter and area?

Perimeter is the distance around the outside of a shape, while area is the measure of the space inside a shape. In other words, perimeter is the length of the boundary of a shape, while area is the amount of surface that the shape covers.

5. Can the perimeter of a pentagon be greater than its area?

Yes, it is possible for the perimeter of a pentagon to be greater than its area. This can occur if the pentagon is stretched out to have longer sides, making the perimeter longer, but the area does not increase proportionally.

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