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 __%.
Area of similar figures are proportional to the square of their corresponding sides
area of smaller pentagon : area of larger pendagon = 1^2 : 4^2 = 1 : 16
make use of this in your answer.
Can you please help me further?
To determine the new size of the sides of the pentagon after quadrupling, you need to multiply each side length by 4. So, if the original side length is "x", the new side length would be 4x.
To find out how many times larger the sides are, divide the new side length by the original side length. In this case, (4x/x) = 4. Therefore, the sides are now 4 times as large as before.
To calculate the change in the area, we need to consider that the area of a regular pentagon can be found using the formula (1/4) * √(5(5 + 2√5)) * s^2, where "s" is the side length.
If the original area is "A," the new area would be (1/4) * √(5(5 + 2√5)) * (4x)^2 = 16A.
So, the area is now 16 times as large as before.
To determine the increase as a percentage, subtract the original area from the new area, divide by the original area, and multiply by 100.
Increase% = ((16A - A) / A) * 100 = (15A / A) * 100 = 1500%.
Therefore, the area has increased by 1500%.