Answer:
Area = 26 un^2, Perimeter = 4 + 13√2 + √26 un
Explanation:
ABCD is a trapezoid because there are 2 parallel bases with one longer than the other.
The formula for a trapezoid is 1/2 (a+b) h
There are multiple ways to solving this problem, such as finding the individual areas of the triangles and rectangle within and adding it up. If you've done part 15-17, you can just add up the areas you got there. However, I will show the method with the trapezoid area formula.
We need to take advantage of the distance formula in this problem, which is √( (x2-x1)^2 + (y2-y1)^2 )
First for the smaller base the 2 points we have are (0,3) and (4, -1)
The length between those 2 points would be: √( (4)^2 + (-4)^2) which is √32.
Next we have the larger base and the 2 points are (-5, 4) and (4, -5)
The length between these points is: √( (9)^2 + (-9)^2) = √162
Lastly, we have the height which requires the 2 points (0, 3) and (-2, 1)
The length is √( (-2)^2 + (-2)^2 ) = √8
Now to multiply it all — 1/2 (√32 + √162) * √8 which simplifies to 1/2 (4√2 + 9√2) * √8 --> 1/2 (13√2) √8 --> 13/2 * √(2*8) --> 13/2 * 4 = 26
Now for the perimeter, the 2 sides we still need to find are the 2 legs.
The first leg requires the 2 points (-5, 4) and (0, 3), and the length is √( (-5)^2 + (-1)^2) = √26.
The second leg has the points (4, -1) and (4, -5), so the length is 4 (we don't need the distance formula here because we can just count units)
Now to sum it all up (the 2 bases + the 2 legs): 4√2 + 9√2 + √26 + 4 = 4 + 13√2 + √26
Hope this helps :)