area of heptagon?

Question

how do you find the area of a heptagon?

the one i have has 1 side length of 22.15. the radius is 23.
what's the area of it?

Answer 1

You can use trigonometry to derive the formula of a regular heptagon as:

(7/4)s^2 * cot(pi/7)

Resolving the constants, this is about 3.634s^2.

Answer 2

The perimeter is the total length of the all the sides (P=Length of sides x number of sides). A regular heptagon is a 7 sided shape. Now for the area. You can split a heptagon into triangles using the apothem to make them into right-angled triangles, so there 2 triangles on each side and a total of fourteen triangles. Each triangle has the sides of 12cm (the apothem), 6cm (the half the side of the heptagon), and one unknown side (connecting the centre of the heptagon to the corner nearest to the apothem). You can use Pythagoras' theorem to find the unknown. You only need to find the area of one triangle and then times it by 14 (number of triangles that can be in there) and that will be the area of the heptagon. Now go work it out yourself. Give a man a fish, he will be fed for a day. Teach a man to fish, he will be fed for a lifetime.

Answer 3

divide it into triangles and calculate their areas separately? then just add them up, only way i can think of

so 1/2 (bh)

[1/2(22.15*23) ]*7 whatever that turns out to be

Answer 4

R^2 Nsin(2pi/N)
--------------------
2

23^2 7 sin(2pi/7)
---------------------
2

area = 1447.560989