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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!

 #1
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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
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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
 #3
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Thank you!


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