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
btw the radius is 4 feet.
https://www.usatestprep.com/modules/gallery/files/25/2560/2560.png
here is the picture link
1 answer:
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
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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Answer:
The turns of a graph is represented by the number of maximum or minimum that the function has.
If we differenciate f(x) we get:
f'(x)=4x^3+6x
f'(x)=2x(2x^2 + 3)
Therefore f'(x) =0, when x=0. Given that negative roots are not defined.
Therefore, the number of turns will be given by the number of solutions of f'(x) which is 1.
Attached you find the graph of the function which confirms the number of turns.
If the function had other solutions, the maximum number of turns it could have is 3! because f'(x) is a third degree polynomial, therefore it can't have more than 3 solutions!
