# Math

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I am to find the area of a square. It is cut in half and the line is measured at 6 square root 2. It also says that the two triangles are equallateral triangles. I know that the equation for a equalateral triangle is
A = the square root of 3 times s squared / 4

How would I solve this so that I can have the area of the square?

• info needed -

Using one single cut, I can cut a square into two isosceles triangles, but not two equilateral triangles.

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Oh, I guess I assumed that the triangle was and equilateral triangle because the only other information it gave me was that it had an angle of 45 degrees in the corner that was split.

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So that makes two isosceles right triangles. The hypotenuse (the longest side) is the cut, right? Draw a little diagram to confirm that.

The area of an isosceles right triangle (i.e. 45°,90°45°) is equal to the hypotenuse²/4. The hypotenuse is the cut, or the side that joins the two 45° angles.

Take it from here, and post your answer for verification if you wish.

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A = 6 square root 2 to the power of 2 / 4
A = 12/4
A = 3

Then to find the area of the square I would multiply 3 time 2 to equal 6

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A = (6 square root 2) to the power of 2 / 4
=6²*(√2)²/4
=?

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Oh ok I didn't square both the 6 and the square root 2...that makes sense. Thank you.

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You're welcome!