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Find Area of Square from Diagonal | Geometry
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How do we find the area of a square from the diagonal? This is a simple application of the Pythagorean theorem, and we'll derive a formula for it in today's video geometry lesson!
A square has 4 right angles, and its diagonals are congruent (this is easily shown by the SAS triangle congruence postulate). When we draw a diagonal of a square, we cut the square into two right angles. We can then apply the Pythagorean theorem to either of these right triangles to relate the diagonal length to the side length of the square. The side length squared is the area, which is the final relationship we need to know.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
+WRATH OF MATH+
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A square has 4 right angles, and its diagonals are congruent (this is easily shown by the SAS triangle congruence postulate). When we draw a diagonal of a square, we cut the square into two right angles. We can then apply the Pythagorean theorem to either of these right triangles to relate the diagonal length to the side length of the square. The side length squared is the area, which is the final relationship we need to know.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
+WRATH OF MATH+
Follow Wrath of Math on...
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