+1452 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!
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.
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.
