Question

"""Square area formula in terms of diagonal.

a) (A = {1}{2}d^2)
b) (A = {1}{2}sqrt{2}d^2)
c) (A = {1}{2}d)
d) (A = {1}{2}sqrt{2}d)"""

Answer 1

The correct formula to calculate the area of a square in terms of its diagonal is (a) A = 1/2d², as derived using the Pythagorean theorem.

Step-by-step explanation:

The question is asking for the formula to calculate the area of a square in terms of its diagonal. To solve for the area (A) of a square in terms of the diagonal (d), you can use the Pythagorean theorem. A square can be divided into two equal right-angled triangles, and the diagonal serves as the hypotenuse for both triangles. According to the Pythagorean theorem, for a right-angled triangle with sides a, a, and diagonal (hypotenuse) d, the relationship is a² + a² = d². Combining the sides, we have 2a² = d², so a² = d²/2. However, the area of the square is a², thus A = d²/2.

In this case, a represents the side length of the square, and as such, the area in terms of diagonal will be A = d²/2. Therefore, the correct answer from the provided options is a) A = 1/2d² since this is the only option that correctly represents the area of a square in terms of its diagonal.