I know this question has been answered, but I still don't understand. Please help.
The sides of the pentagon are quadrupled, so they are now __ times as large. This means the area is now __ times as large. This is equivalent to an increase of __%.
This is the third time this question has been answered since yesterday, each time posted by students
with a different name. Are you just switching names?
https://www.jiskha.com/questions/1825627/the-sides-of-the-pentagon-are-quadrupled-so-they-are-now-times-as-large-this-means
I don't understand the solution, can you help me?
Ok
The pentagon is made up of 5 equal isosceles triangles with a central angle of 72°, right?
Each base angle = 52°
if we let the base = 2, then the height will be:
tan52 = h/1
h = tan52
and the area of one triangle = (1/2)(2)tan52° = tan52
area of whole pentagon = 5tan52
so we are quadrupling the base, so the base is now 8
and the height is 4tan52°
area of whole pentagon = (1/2)(8)20tan52 = 80tan52
how many times larger is 80tan52 than 5tan52 ????
80tan52/(5tan52) = 16
To understand this question, we need to break it down and look at the relationship between side lengths, area, and percent increase.
Let's start with the first part: "The sides of the pentagon are quadrupled, so they are now __ times as large."
To determine how much larger the sides are after being quadrupled, we need to calculate the multiplication factor. Since "quadrupled" means multiplied by 4, the sides are now 4 times as large as their original length.
Moving on to the second part: "This means the area is now __ times as large."
The relationship between the sides of a polygon and its area depends on the shape. For a regular pentagon, the area is proportional to the square of the side length. So, if the side length is quadrupled, the area will be quadrupled squared. In other words, the area becomes 4^2 = 16 times as large as the original area.
Finally, we come to the third part: "This is equivalent to an increase of __%."
To calculate the percent increase, we need to find the difference between the new and original area, divide it by the original area, and multiply by 100%. In this case, the new area is 16 times the original area, so the increase is 16 - 1 = 15 times the original area. The percent increase is (15/1) * 100% = 1500%.
To summarize:
- The sides of the pentagon are now 4 times as large.
- The area is now 16 times as large.
- This represents a 1500% increase in area.