Basic Geometry : Squares
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Example Questions
Example Question #21 : Squares
A square has side lengths of 
Finding the diagonal of a square is the same as finding the hypotenuse of a triangle, and uses the Pythagorean Theorem. (Imagine the square being sliced diagonally into two triangles, for you visual learners.) Within this theorem, both a and b are the same number, since the sides of a square are equal.
Example Question #21 : Squares
Find the length of the diagonal of a square whose side length is 3.
To find a diagonal of a square recall that the diagonal will create a triangle in the square for which it is the hypotenuse and the side lengths will be the other two lengths of the triangle.
To solve, simply use the Pythagorean Theorem to solve.
Thus,
Example Question #21 : Squares
Find the length of the diagonal of a square with side length 2.
To solve, simply use the Pythagorean Theorem. Thus,
Remember, that when simplifying square roots, you can only pull a number out if you have two factors of it. That is why I grouped the end of this answer the way I did so you could see that since I had two squared, I could pull one out, one disappears, and the two on the outside of the parenthesis remains under the radical.
Example Question #21 : Squares
The area of a square is 
Since the area is 25 square meters and we know it's a square, the length of each side is 5 meters, since 5 x 5 = 25.
To find the length of the diagonal, use the Pythagorean theorem:
Example Question #21 : Squares
What is the length of the diagonal of a square with 3-inch sides?
To solve, use the Pythagorean Theorem:
Example Question #22 : Squares
True or false: The length of a diagonal of a square with sides of length 1 is 
False
True
False
A square is shown below with its diagonal.
Each of the triangles formed is an isosceles right triangle with congruent legs - by the 45-45-90 Triangle Theorem, they are 45-45-90 triangles. Also by the 45-45-90 Triangle Theorem, the diagonal, the hypotenuse of each triangle, measures 
Example Question #23 : Squares
Consider the square 
Recall that the side lengths of a square are each congruent; recall further that the angles in a square are each right angles. Hence, the diagonal 
Hence, the length of the diagonal 
Example Question #27 : Squares
A square has a side length of 12 inches. What is the length of the diagonal across its face?
None of the other answers.
Squares have four congruent sides. If one side is 12, the other sides must be as well. Since the diagonal makes a right triangle with the other sides we can use Pythagorean theorem to find the diagonal.
Take the square root of both sides:
The length of the diagonal is 17 inches.
Example Question #22 : Squares
The sides of a square garden are 10 feet long. What is the area of the garden?
The formula for the area of a square is
where 
Example Question #681 : Plane Geometry
The length of line 
Cannot be determined
Since 
We get area by multiplying length by width (or base by height, if you prefer), since all sides are equal, it looks like this:
Don't forget, the units are SQUARE INCHES.
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