SOLUTION: The area of a square with diagonals of 10 cm long

Question 620756: The area of a square with diagonals of 10 cm long
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
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We can solve this problem using the equation from the Pythagorean Theorem: . First, we'll find the side length of the square. Then we'll find the area of the square using the side length.
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Draw a picture of a square.
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Now draw in one of the diagonals from one corner to the opposite corner (for example, from the upper left corner to the lower right corner.)
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Notice that you have two triangles inside the square. These are both right triangles because every corner of the square is a 90-degree angle. Both triangles have the same shape, except that one is rotated upside down. The diagonal makes the hypotenuse of both triangles.
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Let's have the variable s be the length of the sides of the square.
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Look at one of the right triangles. Notice that both legs have a length of s, and the hypotenuse has a length of 10.
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Use the the Pythagorean Equation. Substitute s for a and b, and 10 for c.
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Solve for s.
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Now we know that the side length is . We can use the formula for the area of a square.
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Substitute for s in the formula.
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Taking the square root of a numer and squaring a number reciprocal operations--they undo each other (like adding and subtracting te same number.) This means that squaring the square root of 50 gives you 50.
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The area of the square is 50 square centimeters.
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Hope this helps, Feel free to email if you have questions about this.
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Ms.Figgy
math.in.the.vortex@gmail.com
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