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, let's label the points where the squares intersect as points I and K.
Since JH=5 and JC = 8, we can calculate the length of JI by using Pythagorean theorem in triangle JCH:
CH^2 = JH^2 + JC^2
CH^2 = 5^2 + 8^2
CH = √(25 + 64)
CH = √89
As JI is parallel to CH and the line segment JI is the same as CH, JI = CH = √89
To find IK, we can use Pythagorean theorem in triangle CIJ:
IJ^2 = IC^2 + CJ^2
IJ^2 = √89^2 + 8^2
IJ = √(89 + 64)
IJ = √153
The area of the shaded region is equal to the area of square ABCD minus the area of the four triangles with base IJ and height KC:
Area of shaded region = Area of square ABCD - 4 * (0.5 * base * height)
Area of shaded region = (IJ)^2 - 4 * (0.5 * IJ * KC)
Area of shaded region = √153^2 - 4 * (0.5 * √153 * 8)
Area of shaded region = 153 - 4 * (4√153)
Area of shaded region = 153 - 16√153
Therefore, the area of the shaded region is 153 - 16√153.