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. You can use the to upload a picture of your work
First, we need to find the side length of square EFGH. Since JC is a diagonal of square EFGH and is 8 units long, we can use the Pythagorean theorem:
\(JC^2 = EF^2 + JH^2 \\
8^2 = EF^2 + 5^2 \\
64 = EF^2 + 25 \\
EF^2 = 64 - 25 = 39 \\
EF = \sqrt{39} \approx 6.24\)
Since EFGH is a square, all sides are the same length, so each side is approximately 6.24 units.
The area of square EFGH is \(6.24^2 \approx 38.94\).
Next, we need to find the area of square ABCD. Since JH is 5 units long, each side of square ABCD is 5 units long. Therefore, the area of square ABCD is \(5^2 = 25\).
The shaded region is the difference between the area of square EFGH and square ABCD:
\(38.94 - 25 = 13.94\).
Therefore, the area of the shaded region is approximately 13.94 square units.