Question

find the area of a regular octagon each of whose sides measures 6 cm?????

Answer 1

hello.....,

in the photo I have divided the octagon into 8 isosceles triangle.

And we have found that the every measure of the angle= 45degree.

then we have taken an altitude from the apex to the base of triangle.

Altitude divided the measures into half means....our 45 degree become 22.5 degree.

and 6 cm become 3cm ......

then we taken the our formed triangle outside for better looking.

after that,

I have told you that a means apothem..and now we have to find the value of a .

Using Trigonometric,

Tan Titha= opposite/ adjacent

tan 22.5 = 6/a ........
( because 6 is our opposite side and a is adjacent side of angle 22.5 degree.)

tan (22.5) can be written as 0.4142

0.4142/1 = 6/a

0.4142a = 6. ...........( cross multiply)

a = 6/0.4142

a= 14.5

therefore apotham = 14.5

now we have all required values.

Area = perimeter*apotham/2

Perimeter = 6*8

= 48.

hence,

Area= 48*14.5/2

= 696/2

= 348

therefore Area = 348cm^2

I hope it will helps you...

thanks for asking questions....

Answer 2

Answer:

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