Answer:
173.97
Explanation:
so first we have to find the other side length by using the law of cosines. using this law we are able to find a length of a side with the opposite angle measurement and the 2 side lengths.
first we are going to set up out problem...
so lets say that the opposite side is going to be a the right side is going to be b and the left side is going to be c
a²=b²+c²-2·b·c·cosФ
so now we plug in the numbers
a²=26²+26²-2·26·26·cos(31)
simplify like this
a²=26²+26² =1352
- (don't forget the subtraction sign)
2·26·26·cos(31) = 1158.89
now we plug that back in to get...
a²=1352-1158.89
now we do a little math
a²= 193.11
then we square root to get the a by itself and we get (√a²= √193.11)
and we get a = 13.89
now we have all of the side length the have to find the height to finish our problem. we are going to cut this shape in half to make a right triangle
now out bottom length will be 6.94
now we use the pythagorean theorem
a²+6.94²=26²
now in this situation don't get confused a is going to be out height
now we solve
a²+48.16=676
-48.16 -48.16
a²=627.84
then the square root each side........
√a²=√627.84
and we get
a=25.05 this is our height
now to solve for the area
(b · h)/2
plug in
(13.89 · 25.05)/2
347.94/2
173.97 there is our answer