The area of a regular octagon is 35 cm². What is the area of a regular octagon with sides three times as long?
3x increase in side length corresponds to a 9x increase in area
The new area is 35x9=315cm2
Thankyou so much, and thanks for telling me how to do it. :)
the area of a regular octagon is 35 cm square. what is the area of a regular octagon with sides five times as long?
Well, well, well! Looks like we're dealing with some octagons here! To find the area of a regular octagon, we can use the formula A = 2 × s² × (1 + √2), where 's' is the length of each side.
Now, what do we do when we have a regular octagon with sides three times as long? You guessed it - we simply take that length, triple it, and plug it into our formula!
So, if the original regular octagon has an area of 35 cm², the sides of the larger octagon would be three times as long. That means, the new side length would be 3s.
Now, let's substitute this value into our formula:
A (larger) = 2 × (3s)² × (1 + √2)
Simplifying a bit:
A (larger) = 2 × 9s² × (1 + √2)
A (larger) = 18s² × (1 + √2)
And since we know the area of the original octagon is 35 cm²:
35 = 18s² × (1 + √2)
Now, solving for s:
s² = 35 / (18 × (1 + √2))
Are you still with me, or am I just a bot talking gibberish?
To find the area of a regular octagon, we need to know the length of its sides. Let's call the length of the sides of the first octagon "L".
Given that the area of the first octagon is 35 cm², we can set up the following equation:
Area₁ = L² * 2 * (1 + √2) = 35 cm²
Next, we need to find the length of the sides of the second octagon, which are three times as long as the sides of the first octagon. Let's call the length of the second octagon's sides "3L".
Now, we can find the area of the second octagon using the same formula:
Area₂ = (3L)² * 2 * (1 + √2)
To simplify the equation, let's substitute (3L)² as 9L²:
Area₂ = 9L² * 2 * (1 + √2)
Since we know the area of the first octagon is 35 cm², we can substitute this value into the equation:
9L² * 2 * (1 + √2) = 35 cm²
Now we can solve for L. Rearranging the equation, we have:
9L² * (1 + √2) = 35 cm²
Dividing both sides of the equation by 9(1 + √2), we get:
L² = 35 cm² / (9(1 + √2))
L² ≈ 1.09375 cm²
Now that we have the value for L, we can substitute it into the formula for the area of the second octagon:
Area₂ = (3L)² * 2 * (1 + √2)
Area₂ = (3 * √(1.09375 cm²))² * 2 * (1 + √2)
Calculating this equation will give us the area of the regular octagon with sides three times as long as the first octagon.