Question

Find the length of the side of a regular heptagon that is inscribed in a circle of radius 7 cm.

Answer 1

what are the answers???

Answer 2

the answer is 28

Answer 3

how did you get it?

Answer 4

like this

Answer 5

14x2=28

Answer 6

Hmm...not sure I agree with that...but draw a diagram of the circle and the pentagon inside it.

Divide the circle by the number of sides of your figure, heptagon = 7
So each internal angle at centre of circle is (360/7) = 51.43 degrees. Half-angle = 25.71 degrees.
Each triangle making up the heptagon has two sides equal to the radius.
If radius = r, then length of half-side of heptagon = rsin25.71
Length L of one side of heptagon = 2r.sin25.71.
If r = 7,
L = (2 x 7) x sin25.71 = 14 x 0.43388 = 6.074cm

And I believe that would be your answer...I am rusty on questions like these but I believe this is how it is solved

It wouldnt make sense to be 28cm because that would clearly break out of the circle...thus it wouldn't be inscribed

Answer 7

Ok. thanks :)

Answer 8

No problem :)