All categories

3 years ago

Find the area of a 8-gon with radius length 6. Round to a whole number.

Mathematics

1 answer:

djyliett [7]3 years ago

7 0

Answer:

Area = 102

Step-by-step explanation:

Length 1 side of the octagon.

The formula for the side of an octagon (given the radius of 6) is

s^2 = 2*R^2(1 - cos(45) )

s^2 = 2*6^2(1 - sqrt(2)/2)

s^2 = 72 ( 1 - 0.707)

s^2 = 72*0.2929

s^2 = 21.09

s = sqrt(21.09)

s = 4.5922

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

Height of one triangle =

H = R * cos(22.5)

H = 6 * 0.9329

H = 5.5433

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

Area of 1 triangle

Area = 1/2 * s * h

Area = 1/2 * 4.5922*5.4433

Area = 12.7279

Area of 8 triangles

Area of 8 triangles = 1 triangle * 8

Area of 8 triangles = 101.82

Rounded that comes to 102

Comment

I'm sure you can find a formula for this on the internet, but it this is the way the formula works and if you break it down step by step, you can see how the formula works.

You might be interested in

What is the value of x in the figure ? In this diagram,

riadik2000 [5.3K]

9514 1404 393

Answer:

E. 25/4

Step-by-step explanation:

The right triangles are similar so the sides are proportional.

short side/hypotenuse = x/10 = 10/16

x = 100/16 = 25/4 . . . . . . multiply by 10

3 0

3 years ago

Which answer doesn't equal 64? A. 2^{6} B. 4^{3} C. 8^{2} D. 32^{2}

klemol [59]

First one is 64
second one is 64
third one is 64
so your last one is it because 32 * 32 is way higher than 64

6 0

4 years ago

Read 2 more answers

Find a rectangular equation. X = 3tan t, Y = 2sec t, for in (−π /2 , π /2 )

anzhelika [568]

Answer:

Step-by-step explanation:

$x= 3tan(t) \rightarrow tan(t) = \frac{x}{3} \rightarrow tan^2(t) = \frac{x^2}{9}$

$y= 2sec(t) \rightarrow sec(t) = \frac{y}{2} \rightarrow sec^2(t) = \frac{y^2}{4}$

$sec^2(t) -tan^2(t) =1$

$\frac{y^2}{4} -\frac{x^2}{9} =1$

is the rectangular equation of the parameter functions.

also, it is a hyperbola. The condition $-\pi/2 < t$ limit x from 0 to infinitive

7 0

4 years ago

How many degrees is 25/360 of a full turn

ludmilkaskok [199]

If a full turn is 360 degrees then it is 25 degrees

8 0

3 years ago

Read 2 more answers

A man buys a car for $33,000 with no money down. He pays for the car in 48 equal monthly payments with interest at 9% per annum,

Crazy boy [7]

Answer:

Man has to pay $1921.19 per month.

Step-by-step explanation:

The formula of Compound Interest is:

$A = P(1+\frac{r}{n})^{nt}$

where A = Amount

P = Principle

r = rate

n = Number of Compounding per year

t = total number of year

Here, A = 33,000, r = 9% = 0.09, n = 12(monthly), and t = 48(48 months).

Putting all these values in above formula:

$33000 = P(1+\frac{0.09}{12})^{12\times4}$

⇒ $33000 = P(\frac{12.09}{12})^{48}$

⇒ $33000 = P(1.0075)^{48}$

⇒ $33000 = P(1.4314)}$

⇒ P = 33000 ÷ 1.4314 = 23054.35

Monthly payment = 23054.35 ÷ 12 = 1921.19

Hence, Man has to pay $1921.19 per month.

8 0

4 years ago