Directions: Please find the area and side length of square ACEG. Please show all of your work (all of your calculation) in the grey box below.

9514 1404 393

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.

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

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step-by-step explanation: