If a heptagon has an area of 105in^2, what is the measure of one side?

Question

I have to use something similar to this : 360 / 5 = 72

72 = top of one angle

180 - 72 = 108 , 108 / 2 = 54

54 = side angle

Area = 1/2* Base* Height

tan (54) = h (3/2)

h = 1.5*tan (54), h = 2.06

A = 1/2 (3) (2.06)

A = 3.09

3.09 * 5 = 15.45

Answer 1

It has to be a REGULAR 7-gon or else nothing can be done!!!

Assuming so....

The area of each of the 7 slices is 105/7 = 15

Side measure is X.

The total number of degrees is (7-2)*180 = 5*180 = 900

900/7 = 128 and 4/7 degrees at each vertex

Draws the perpendicular height from center to edge,

each pie slice forms 2 congruent right triangles with

side measures X/2 at the base, height H, and congruent

sides y The base angles are 64 and 2/7 degree each.

(1/2)X*H = 15

XH = 30

H = 30/x

tan (64 and 2/7) = 2H/x

1.0382606982861682835817694307429.... = h/x

1.0382606982861682835817694307429.... = h/x

. = 30/x^2

x^2 = 28.894771284578659929741183418...

x = 5.3753583255864644413808265184269....