The area of a regular octagon is 25. What is the area of a regular octagon with sides five times as large as the sides of the first octagon?

Area of octagon:

A=2*[1+sqroot(2)]*a^2

A1=Area of first octagon

A1=25

A2=Area of five time lager side octagon

A1=2*[1+sqroot(2)]*a^2

A2=2*[1+sqroot(2)]*(5a)^2

A2=2*[1+sqroot(2)]*25*a^2

A2/A1=2*[1+sqroot(2)]*25*a^2/2*[1+sqroot(2)]*a^2= 25

A2/A1=25

A2=25*A1= 25*25= 625

In google type:

Octagon

When you see list of results click on wikipedia

To find the area of the second octagon with sides five times larger, we need to use a scaling factor of 5.

Here's the step-by-step process to calculate the area of the second octagon:

1. Begin by finding the area of the first octagon.
- The formula for the area of a regular octagon is given by:
Area = (2 + 2√2) * s^2, where s is the length of a side of the octagon.
- Since the area of the first octagon is given as 25, we can set up the equation:
25 = (2 + 2√2) * s^2.

2. Solve the equation to find the length of a side of the first octagon.
- Divide both sides of the equation by (2 + 2√2):
25 / (2 + 2√2) = s^2.
- Take the square root of both sides to find the length of a side, s:
s = √(25 / (2 + 2√2)).
- Calculate the value of s using a calculator.

3. Calculate the length of a side in the second octagon.
- Multiply the side length of the first octagon (found in step 2) by the scaling factor of 5:
5 * s = 5 * √(25 / (2 + 2√2)).

4. Find the area of the second octagon using the formula for the area of a regular octagon.
- Apply the formula for the area of a regular octagon with the calculated side length from step 3:
Area = (2 + 2√2) * (5 * s)^2.

By following these steps, you can determine the area of the second octagon with sides five times larger than the first octagon.