Basic Geometry : Quadrilaterals
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Example Questions
Example Question #56 : How To Find The Length Of The Side Of A Square
The area of a square is 36. Find the length of its sides, 
The area of a square is given by the formula
where 
We were given
so to find 
Example Question #57 : How To Find The Length Of The Side Of A Square
Know that in a Major League Baseball infield the distance between home plate and first base is 90 feet and the infield is a perfect square.
If a field designer accidentally designs an infield with an area of 3600 Square Feet, but remembers to make the infield a perfect square, what is distance between home plate and first base?
The answer can be found by knowing that the area of 3600 square feet is smaller than the typical area of 8100 square feet.
This means the length of the square's sides must be smaller than 90 feet.
Then you can check by finding the area of the squares that would be formed by the lengths that are lower than 90 feet. 60 feet is the correct answer because 60x60=3600 Square Feet.
Example Question #571 : Quadrilaterals
True or false: A square with diagonals of length 2 has sides of length 
False
True
True
A square is shown below with its diagonal of length 2.
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, each leg of the triangle has length equal to the hypotenuse divided by 
Rationalize the denominator by multiplying both halves of the fraction by 
Example Question #572 : Quadrilaterals
True or false: A square with area 49 has sides of length 7.
False
True
True
Given the length of each side of a square, the area of the square is the square of this length. Therefore, to find the sidelength, take the square root of the area. The area of the square is 49, and 
Example Question #57 : How To Find The Length Of The Side Of A Square
If the area of a square is 
If we are given the area of a square, in order to find the length of a side we must take the square root of the area. We need to know that the formula for area of a square is
(where s is side) so we plug in 400 for the area and we have
To solve for s we must take the square root of both sides
and we get
When taking square roots we reject the negative if we are working with measurements. Our final answer is 20 inches.
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