Table Of Contents
What is Square
A square is a special case of a quadrilateral all of whose sides are equal, and each angle is 90°.
Perimeter of square
We now know that the perimeter is the length of the boundary of any geometric shape. We discussed earlier that the square is made up of 4 equal sides, so the sum of all the four equal sides gives us its perimeter.
The formula for perimeter of a square is:
P = 4 \(\times\) s
Where s is the length of one of the sides of the square.
The side and perimeter can be expressed in the following units:
millimeter(mm), centimeter(cm), meter(m), kilometer(km), inch(in), feet(ft), yard(yd), mile(mi) and so on.
Solved Examples
Example 1: Find the perimeter of a square whose side length is 4 inch.
Solution:
P = 4 \(\times\) s Write the formula for perimeter of square
P = 4 \(\times\) 4 Substitute 4 for s
P = 16
So, the perimeter of a square is 16 inches.
Example 2: Find the perimeter of a square desk whose edge length is 3 feet.
Solution:
P = 4 \(\times\) s Write the formula for perimeter of square
P = 4 \(\times\) 3 Substitute 3 for s
P = 12
So, the perimeter of a square desk is 12 feet.
Example 3: The perimeter of a square shaped garden is 40 yards. Find the side length of the garden.
Solution:
P = 4 \(\times\) s Write the formula for perimeter of square
40 = 4 \(\times\) s Substitute 40 for P
\(\frac{40}{4}\) = \(\frac{4\times s}{4}\) Divide each side by 4
10 = s
So, the side length of the garden is 10 yards.
Example 4: Jacob walks a total of 3200 meters on a square shaped path around the park. If he covered the entire path while covering this distance, then what is the length of one of the sides of the path.
Solution:
Jacob, walking along the edges of the square shaped park, completes one round, which is the perimeter of the park.
As the park is square shaped,
The perimeter of the park(P) = 4 length of one side of path(s)
3200 = 4 \(\times\) s Substitute 3200 for P
\(\frac{3200}{4}\) = \(\frac{4\times s}{4}\) Divide each by 4
800 = s
So, the length of one side of the path is 800 meters.
Example 5: James has a square plot with sides that are 50 feet in length. What is the boundary length of the plot? If fencing material costs $10 per foot, then find the costing of fencing the plot.
Solution :
Boundary length is equal to perimeter:
P = 4 \(\times\) s Write the formula for perimeter of square
P = 4450 Substitute 50 for s
P = 200
So, the length of his boundary is 200 feet.
Now to find the cost of fencing we need to multiply the perimeter found by the rate of fencing.
= 200 \(\times\) 10
= $2000
Therefore the cost of fencing the square plot that James has is $2000.
There are three types of parallelograms:
- Rectangle
- Rhombus
- Square
A square has four angles, each angle measuring 90°, but on the other hand, a rhombus does not.
Yes, all the properties of a rectangle are found in squares.
- Both are parallelograms.
- Both have sides that are equal in length.
- Diagonals are perpendicular bisectors in both of these geometric shapes.
Area of square = \(s^2\), where s is the length of the side of the square.
Perimeter is a measure of distance, so all the units of distance are used as units to express perimeter. Such as millimeter(mm), centimeter(cm), meter(m), kilometer(km), inch(in), feet(ft), yard(yd), mile(mi) and so on.