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tensa zangetsu [6.8K]
3 years ago
13

The polygon in the diagram is a regular octagon with center A. Find the area of the octagon to the nearest tenth of a foot. A) 2

2.6 ft2 B) 45.3 ft2 C) 90.5 ft2 D) 121.8 ft2
btw the radius is 4 feet.

https://www.usatestprep.com/modules/gallery/files/25/2560/2560.png
here is the picture link

Mathematics
1 answer:
IRISSAK [1]3 years ago
4 0
Method 1: In order to find out the area of an octagon with a radius of 4 feet, we have to split the whole figure into 8 equal isosceles triangles.
Therefore, 
We will find out the area of one triangle and multiply the area with 8 to, figure out the area of the whole octagon there are 8 similar triangles and all of them will have the same area.

Method 2: From method 1, it would take time as there are too much of calculation, therefore we would go for the shortcut using the formula:

Area = 2√2 × r²

where r<span> is the radius of the octagon.
Substituting the values,
We get:
             </span>Area = 2√2 × 4²
             Area = 2√2 × 16
             Area = 2× 1.41 × 16 
             Area = 2.828 × 16 
            Area = 45.25

Rounded to the nearest tenth:

Area = 45.3 ft²


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I got this answer from the link: brainly.com/question/2165977?entry=7190 I give them credit for this, as they were the original. For future reference, you can search your question at the top, and if someone has already answered that question and it is the same as yours, than you can use that, and thank them, etc.  I hope this helps!<span />
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Answers:

Lower bound = 41.3

Upper bound = 41.5

===========================================================

Explanation:

49.15 is the smallest f can be while 49.24 is the largest it can be. Well technically we could have something like 49.2499 or 49.24999 and so on. We slowly approach 49.25 but never actually get there

So the variable f is between 49.15 and 49.25 inclusive of the first value but excluding the second value. We can write it as 49.15 \le f < 49.25

For similar reasoning, 7.75 \le g < 7.85

-----------------

If we wanted to subtract those variables and get the smallest result possible, then we need to pick values that are closest together. It might help to set up a number line.

This means we'd go for f = 49.15 and g = 7.85

The lower bound for f-g is f-g = 49.15-7.85 = 41.3

In contrast, the upper bound is when the two variables are spaced as far apart as possible. The upper bound is f-g = 49.25 - 7.75 = 41.5

7 0
2 years ago
Read 2 more answers
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