Question

The diagonal of a square unit is x units. What is the Area of the square in terms of x

Answer 1

The diagonal of a square is:

d^2=s^2+s^2

d^2=2s^2  we are told that d=x  so

x^2=2s^2

s^2=(x^2)/2

And since the area of a square is s^2, the area of this square is:

(x^2)/2

Or as it is shown in your answer choices...

(1/2)x^2 square units  (the top answer :P)

Answer 2

The area of a square with a diagonal x is (1/2)x² unit²

Square

A square is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel. All the sides of a square have the same length and each angle measure 90 degrees.

let l represent the length of the side of the square and x be the length of the diagonal. Using Pythagoras theorem:

• l² + l² = x²
• x² = 2l²
• l = x√(1/2)

Area of square = l * l = x√(1/2) * x√(1/2) = x² * 1/2 = (1/2)x² unit²

The area of a square with a diagonal x is (1/2)x² unit²

Find out more on square at: https://brainly.com/question/8429946