ABCD and EFGH are squares. If JH=5 and JC = 8, then what is the area of the shaded region? Show all work in order to recieve full credit.
Since JH = 5 and JC = 8, we can see that JH is one side of square EFGH, and JC is the diagonal of square ABCD.
Let x be the side length of square ABCD, then we can use the Pythagorean theorem to find the side length of square ABCD:
x^2 + x^2 = 8^2
2x^2 = 64
x^2 = 32
x = √32 = 4√2
The area of square ABCD is:
Area_ABCD = x^2 = (4√2)^2 = 32
The area of square EFGH is:
Area_EFGH = (5)^2 = 25
Therefore, the area of the shaded region is:
Area_shaded = Area_ABCD - Area_EFGH
Area_shaded = 32 - 25
Area_shaded = 7
So, the area of the shaded region is 7.