9514 1404 393
Answer:
- area: 100 square units
- side length: 10 units
Step-by-step explanation:
There are a couple of ways to do this. You can find the side length and then the area, or you can find the area and then the side length.
There are a couple of different ways to find the area. Here, we'll subtract the area of the triangles from the area of the larger square.
The larger square has sides of length 6+8 = 14, so its area is 14² = 196.
The area of each triangle is 1/2(6)(8) = 24, so the four of them together have a total area of 4×24 = 96.
Then the area of the smaller square is 196 -96 = 100 square units.
The side length is the square root of that, √100 = 10 units.
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Alternate solution
Using the Pythagorean theorem, you can find the square of the side length (which is the area of the smaller square), and the side length.
AC² = AB² +BC²
AC² = 6² +8² = 36 +64 = 100 = area of ACEG
AC = √100 = 10
