Aregular octagon has an apothem measuring 10 in. and a perimeter of 66.3 in. what is the area of the octagon, rounded to the nearest square inch? 88 in.2 175 in.2 332 in.2 700 in.2

Step-by-step explanation:

The area of a regular polygon is calculated using the formula;

where is the apothem and p is the perimeter.

It was given that, the apothem is, and the perimeter is

We substitute into the formula to obtain;

To the nearest square inch, we have;

The answer is:

From the statement we know that the octagon has a apothem of 10in and a perimeter of 66.3in, and we are asked to find the area of the octagon.

We can use the following formula:

Substituting the given information into the area formula, we have:

Rounding to the nearest number we have that:

331.5 ≈ 332

So, the area of the octagon is:

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geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

step-by-step explanation: