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The diagonal of a square is x units. What is the area of the square in terms of x? One-half x squared square units x squared square units 2x square units One-half x square units

2 Answers

4 votes

Answer:

1/2x^2 square units

Explanation:

User Sergey Novikov
by
8.1k points
5 votes

Answer:


(x^2)/(2) square units [one-half x squared square units]

Explanation:

As shown in the diagram attached to this response,

Since a square has all sides equal, let the sides of the square be each of a units.

The area, A, of the square = a x a = a²

i.e

A = a² --------------(i)

Now,

The diagonal is x units such that applying Pythagoras rule gives;

x² = a² + a²

x² = 2a²

a² =
(x^2)/(2) ----------------(ii)

Substitute the value of a² in equation (ii) into equation (i) to get;

A =
(x^2)/(2)

Therefore, the area of the square is
(x^2)/(2) square units

The diagonal of a square is x units. What is the area of the square in terms of x-example-1
User Ron Reiter
by
8.0k points

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