Answer:
Area = x²/2 square units
Step-by-step explanation:
The key to solving this question is to understand that:
a) the sides of a square are the same length
b) the length of the diagonal may be calculated via Pythagoras' theorem (c² = a² + b², where c is the length of the hypotenuse of a triangle and a and b the lengths of the other two sides)
1. Now, let's call the sides of the square length y and the diagonal is length x.
Using c² = a² + b², we can substitute our values to get:
x² = y² + y²
x² = 2y²
2. Stepping away from Pythagoras' theorem for a little bit, let us think of the general formula for the area of a square:
A (for Area) = a², where a is the length of the sides of the square (which are all of equal length)
Given that we defined our square as having length y, let us substitute this value in to get:
A = y²
3. Now we have two formulas that we can work with:
1) x² = 2y²
2) A = y²
4. Given that A = y², we can say that 2y² = 2A
Therefor, if x² = 2y², then x² = 2A
Thus, if we want to find the formula for area in terms of x, we need to simply rearrange the given formula to make A the subject, giving us:
A = x²/2 square units
Hope that helps :)
