1: How many sides would there be in a convex polygon if the sum of all but one of its interior angles is 1070 degrees?

2: Given that BDEF is a square and AB = BC = 1, find the number of square units in the area of the regular octagon.

Thanks!

AnonymousConfusedGuy
Apr 4, 2018

#1**+1 **

2)

In triangle ABC, Hypotenuse =1^2 + 1^2 =sqrt(2)

Area of Octagon=2[1 + sqrt(2)]*S^2, where S =One side =Sqrt(2)

A =2*2[1 + sqrt(2)]

**A =4[1 + sqrt(2)] units^2 in octagon.**

Guest Apr 4, 2018

#2**+1 **

1) I will take a crack at this one!!

If we try using 1070 degrees as the sum of the interior angles of a convex polygon, we get:

1070 =[n - 2] x 180, where n = number of sides

1070 =180n - 360

180n =1070+360

180n =1430

n = 1430 / 180

n = 7.94 number of sides. Since this is not a whole number, will simply round it up to** 8.**

So, the convex polygon is an **octagon** with sum of its interior angles:

[8 - 2] x 180 =**1080 degrees.**

Guest Apr 4, 2018