The area of a regular octagon is 25 cm2. What is the area of a regular octagon with sides four times as large? Can someone explain how to do this? I keep getting 2500 but i was told it's wrong.
the area grows as the square of the linear ratio
sides 4 times as large means area 4^2 = 16 times as large
25*16=400
Too bad you didn't show your work ...
To find the area of a regular octagon, we need to know the length of one of its sides. In this case, we are given that the area of the original octagon is 25 cm².
To find the length of one side of the original octagon, we can use the formula for the area of a regular octagon:
Area = (2 + 2√2) × s²/2
Where s is the length of one side.
First, let's rearrange the formula to solve for s:
s = √(Area / ((2 + 2√2) / 2))
Plugging in the given area of 25 cm²:
s = √(25 / ((2 + 2√2) / 2))
s ≈ √(25 / (1 + √2))
Now that we know the length of one side of the original octagon, we can find the area of the larger octagon with sides four times as large.
If the length of one side of the original octagon is s, then the length of one side of the larger octagon will be 4s.
To find the area of the larger octagon, we use the formula again:
Area = (2 + 2√2) × (4s)² / 2
Area = (2 + 2√2) × 16s² / 2
Area = (2 + 2√2) × 8s²
Area ≈ (2 + 2√2) × 8 × (s ≈ √(25 / (1 + √2)))²
Calculating this expression will give you the correct area of the larger octagon.
To find the area of a regular octagon, we need to know either the length of its sides or its apothem (the distance from the center of the octagon to the midpoint of any one of its sides).
In this case, let's assume we are given the length of the sides of the first regular octagon, which we'll call "s". The given information is that the area of this first octagon is 25 cm².
Now, we want to find the area of a second regular octagon. But in this case, the length of the sides is four times larger than the original octagon. So, the length of the sides of the second octagon is 4s.
To find the area of the second regular octagon, we need to square the ratio of the side lengths. In this case, it would be (4s/s)² = 4² = 16.
So, the area of the second regular octagon is 16 times larger than the area of the first octagon. Therefore, the area of the second octagon is 16 * 25 cm² = 400 cm², not 2500 cm².
It seems like you made an error when calculating the area of the second octagon. Double-check your calculation, and you should arrive at the correct answer of 400 cm².