Question

No clue how this one works​

Answer 1

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 =
`( 180(n-2))/(n)` n=number of sides

n=10

1 angle of polygon =
`( 180(10-2))/(10)`

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