Answer: 849.5
Explanation:
Make a triangle. 2 of the sides will be 17 The polygon is made up of 10 of those triangles.
A = 10 sides x Area of triangle
A = 10 (1/2) bh
The bottom angle of the triangle can be found by finding the angle of the polygon. The angle of the triangle is 1/2 of the angle of the polygon
1 angle of polygon formula =
n=number of sides
n=10
1 angle of polygon =
1 angle of polygon = 144
1 angle of triangle = angle of polygon/2
1 angle of triangle = 144/2
1 angle of triangle = 72
Draw a line down the middle of the triangle to make 2 right triangles to find height and base. Now use SOH CAH TOA to find the height and base
For height:
sin x = opp/hypotenuse
sin 72 = h/17
h = 17 sin 72
h= 16.17
For base:
cos x = adj/hypotenuse
cos 72 = x/17
x= 17 cos 72
x = 5.25
the base is 2x because we drew a line down the middle to make a right triangle
base= 2x
base = 5.25(2)
base = 10.5
A = 10 (1/2) bh
A = (10) (1/2) (10.5) (16.17)
A= 849.5