Question

Find the area of a square whose diagonal length is 32 CM​

Answer 1

Answer:

512cm^2

Step-by-step explanation:

Let's imagine cutting the square down that diagonal. Now, we have two isosceles right triangles with a hypotenuse with length 32cm. Let's take one of those triangles for now and focus on it. Let's give the one of the legs of a triangle some length x. Since both legs are the same length, by the Pythagorean theorem:

$x^2+x^2=32^2\\\\2x^2=1024\\\\x^2=512\\\\x=\sqrt{512}$

Since this leg makes up one side of the square, we can use it to calculate the area of the square, which is just the side length squared:

$A=(\sqrt{512})^2 = 512$