Basic Geometry : Basic Geometry
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Example Questions
Example Question #431 : Quadrilaterals
A square has diagonals of length 1. True or false: the area of the square is 
False
True
True
Since a square is a rhombus, its area is equal to half the product of the lengths of its diagonals. Each diagonal has length 1, so the area is equal to
Example Question #841 : Basic Geometry
A square has perimeter 1.
True or false: The area of the square is 
False
True
False
All four sides of a square have the same length, so the common sidelength is one fourth of the perimeter. The perimeter of the given square is 1, so the length of each side is 
The area of a square is equal to the square of the length of a side, so the area of this square is
Example Question #842 : Basic Geometry
A square has perimeter 64. True or false: the area of the square is 256.
True
False
True
The length of each of the (congruent) sides of a square is one fourth its perimeter, so multiply 64 by 
The area of a square is equal to the square of the length of a side, so square 16 to get the area:
Example Question #159 : How To Find The Area Of A Square
Assume the length of each side of the square is measured in inches.
If the length of one side of a square is twice the square root of 16, what is the area of the square?
First we need to know that the square root of 16 is 4, because if we work backwards we can see that
So next we double 4 to get 8. Now we know that one side of our square is 8in.
The formula for area of a square is one side to the power of two (side times side) because all sides of a square are equal in length. So now we just take 8in and multiply it by itself (8in x 8in) we get an answer of 
Notice that our answer is in inches squared since we multiplied together two lengths in inches.
Example Question #12 : How To Find The Area Of A Square
A square is circumscribed on a circle with a 6 inch radius. What is the area of the square, in square inches?
24
48
144
36
144
We know that the radius of the circle is also half the length of the side of the square; therefore, we also know that the length of each side of the square is 12 inches.
We need to square this number to find the area of the square.
Example Question #1 : How To Find The Perimeter Of A Square
The length of one side of a square is 6 inches. What is the perimeter of the square?
To find the perimeter of a square, multiply one of its sides by 4.
Example Question #843 : Basic Geometry
The area of square 
Cannot be determined.
We know that 
We also know that since 
To get the measure of any one side of 
Therefore each side of 
To find the perimeter, multiply by 4:
Example Question #844 : Basic Geometry
A square tabletop has an area of 
First find the length of each side.
Take the square root of the area to find the side length:
Since a square has 
Example Question #2 : How To Find The Perimeter Of A Square
A square garden has an area of 64 square feet. If you add 3 feet to each side, what is the new perimeter of the garden?
121
20
25
44
32
44
By finding the square root of the area of the garden, you find the length of one side, which is 8. We add 3 feet to this, giving us 11, then multiply this by 4 to get 44 feet for the perimeter.
Example Question #3 : How To Find The Perimeter Of A Square
The area of the shaded region of a square is 18. What is the perimeter of the square?
36
24
28
20
24
The area of the shaded region, which covers half of the square is 18 meaning that the total area of the square is 18 x 2, or 36. The area of a square is equal to the length of one side squared. Since the square root of 36 is 6, the length of 1 side is 6. The perimeter is the length of 1 side times 4 or 6 x 4.
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