A right pentagonal prism is 10 cm high. If the area of each pentagonal base is 32 cm squared and the perimeter is 20 cm, what are the lateral and total surface areas of the prism?
I tried doing this using the formula shown in my book, but it came out wrong. the formula I was using was for a triangular prism. What the heck is the formula for a pentagonal prism?
triangular prism ---> base is a triangle
pentagonal prism ---> base is a pentagon
So clearly you can't use the triangular prism formula for this question , but you an generalize it looking what it describes.
I don't know what they gave you, but the surface area of a triangular prism consists of
2 congruent triangular bases + 3 congruent rectangles
so the surface area of a pentagon
= 2 (area of the pentagon) + 5rectangles
you are given that the perimeter is 20, so each side of the base is 20/5 = 4, and the height is 10
so the surface area of the 5 rectangles is 5(4)(10) = 200
add the 2 pentagon areas of 32 each for a total of
200 + 64 = 264 cm^2
your text should give you the definitions of lateral and total surface areas, make the necessary adjustments.
http://mathworld.wolfram.com/PentagonalPrism.html
http://easycalculation.com/area/learn-penta-prism.php
Thank you, that makes more sense than what I tried.
its wrong srry
The pentagonal prism below has a base area of 38 units
2
2
and a volume of 368.6 units
3
3
. Find its height.
Let the height of the pentagonal prism be "h" and let the length of one of the sides of a regular pentagon base be "s".
First, we can use the formula for the area of a regular pentagon to find s:
Area of a regular pentagon = (5/4) * s^2 * cot(pi/5)
38 = (5/4) * s^2 * cot(pi/5)
s^2 = 38 * 4 / (5 * cot(pi/5))
s^2 ≈ 12.969
s ≈ 3.6
Now, we can use the formula for the volume of a pentagonal prism to solve for h:
Volume of a pentagonal prism = (5/2) * s^2 * h * cot(pi/5)
368.6 = (5/2) * (3.6)^2 * h * cot(pi/5)
h ≈ 10.9
Therefore, the height of the pentagonal prism is approximately 10.9 units.
The pentagonal prism below has a base area of 45 units
2
2
and a height of 10.3 units. Find its volume.
The volume of a pentagonal prism is given by the formula:
V = (5/2) * base area * height
Therefore, the volume of the given pentagonal prism is:
V = (5/2) * 45 * 10.3 = 1158.75 cubic units
Therefore, the volume of the pentagonal prism is 1158.75 cubic units.
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Alonso sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
349 visitors purchased no costume.
71 visitors purchased exactly one costume.
12 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase no costume as a percent to the nearest whole number.
The total number of visitors to the website in a single day is given by:
Total = 349 + 71 + 12 = 432
The probability that the next person will purchase no costume is the number of visitors who purchased no costume divided by the total number of visitors. So, we have:
Probability of purchasing no costume = 349/432
Converting this to a percentage and rounding to the nearest whole number, we get:
Probability of purchasing no costume = 80%
Therefore, the probability that the next person will purchase no costume is 80%.