find the area of a square whose diagonal is 8m
To find the area of a square given its diagonal, we can use the Pythagorean theorem.
The Pythagorean theorem states that for a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In the case of a square, the diagonal serves as the hypotenuse of two right-angled triangles formed by its sides. Since all sides of a square are equal, let's call the length of each side "s".
Applying the Pythagorean theorem, we have:
s^2 + s^2 = (diagonal)^2
2s^2 = (diagonal)^2
s^2 = ((diagonal)^2)/2
Now, we can substitute the given value:
s^2 = (8m)^2/2
s^2 = 64m^2/2
s^2 = 32m^2
Therefore, the area of the square is s^2 = 32m^2.