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Naya [18.7K]
2 years ago
7

Find the area of the regular octagon.

Mathematics
1 answer:
user100 [1]2 years ago
4 0

Answer:

236.59mm²

Step-by-step explanation:

The formula for the area of a regular polygon is 1/2ap, with <em>a</em> being the apothem and <em>p</em> being the perimeter.

To start, get the perimeter by multiplying 7 (one side of the polygon) by 8 to get 56.

Next, we have to find the apothem (the perpendicular segment from the center of the polygon to one of the sides).

First, create a right triangle on an of the polygon's sides, where the hypotenuse is equal to the radius of the polygon, one of the legs is the apothem, and the other leg is equivalent to half of the side.

Next, using the polygon angle formula (n-2(360)/n), we can get the base angle of the triangle, 1/2(135), or 67.5.

We can use this angle and some trigonometry to find the the apothem.

First, use SOHCAHTOA to figure out if you will use sine, cosine, or tangent (in this case, tangent).

Next, set up an equation using the tangent of 67.5 to find the apothem - tan67.5 = a/3.

And set the equation equal to <em>a</em> (a = 3.5tan67.5).

Now that you have the apothem, plug it into the area formula to get A = 1/2(56)(3.5tan67.5) and solve!

(28)(3.5tan67.5)

(28)(8.4497)

236.59mm²

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Step-by-step explanation:

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What are prime numbers ? And a list of examples ?
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Answer:

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Two angles are complementary angles if the sum of their measure is 90 degrees. Angle A and angle B are complementary angles, and
Marta_Voda [28]
Let's solve this problem step-by-step.

STEP-BY-STEP SOLUTION:

We will be using simultaneous equations to solve this problem.

First we will establish the equations which we will be using as displayed below:

Equation No. 1 -

A + B = 90°

Equation No. 1 -

A = 2B + 12

To begin with, let's make ( A ) the subject in the first equation as displayed below:

Equation No. 1 -

A + B = 90

A = 90 - B

Next we will substitute the value of ( A ) from the first equation into the second equation and solve for ( B ) as displayed below:

Equation No. 2 -

A = 2B + 12

( 90 - B ) = 2B + 12

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B = - 78 / - 3

B = 26°

Then we will substitute the value of ( B ) from the second equation into the first equation to solve for ( A ) as displayed below:

A = 90 - B

A = 90 - ( 26 )

A = 64°

ANSWER:

Therefore, the answer is:

A = 64°

B = 26°

Please mark as brainliest if you found this helpful! :)
Thank you <3
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Kyleigh put a rectangular sticker on her notebook.the hiegth of the sticker measures 18cm.the base is half as long as the height
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Answer:

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Step-by-step explanation:

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s = 6.108652382

Rounded

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3 years ago
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