ABCD and EFGH are squares. If JH= 5cm and JC=8cm, then what is the area of the shaded region?
To find the area of the shaded region, we first need to find the side length of the squares ABCD and EFGH.
Since JH is the diagonal of square EFGH, we can use the Pythagorean theorem to find the side length:
JH^2 = EH^2 + JH^2
5^2 = EH^2 + 5^2
25 = EH^2 + 25
EH^2 = 0
EH = 5 cm
Since EH is the side length of square EFGH, the area of square EFGH is:
Area EFGH = EH^2
Area EFGH = 5^2
Area EFGH = 25 sq cm
Now, since JC is a side of the square ABCD, the area of square ABCD is:
Area ABCD = JC^2
Area ABCD = 8^2
Area ABCD = 64 sq cm
Therefore, the total area of the shaded region is:
Total area = Area ABCD - Area EFGH
Total area = 64 sq cm - 25 sq cm
Total area = 39 sq cm
So the area of the shaded region is 39 square centimeters.