Squares And Rectangles

Finding the Perimeter of Squares and Rectangles

The perimeter is the distance around the edge of an object. We can find the perimeter of any figure. In word problem, there are some key words that let us know that we will be solving the perimeter of a figure. The key words are like edges, fencing and trimare the few names. We can find the perimeter of squares and rectangles. Let’s take an example of a square and see how we can figure out the distance around the edge of the square.

Here is a square. We have only one side with a measurement of 5 feet on it.

A square has four congruent sides. That means that the sides of a square are the same length. Therefore, we only need one side measurement and we can figure out the measurement around the edge of the square.We can figure out the perimeter of the square by simply adding the length of each of the sides. In this example, we would add 5 + 5 + 5 + 5 = 20 feet. 20 feet is the perimeter of this square.

We can use a formula to give us a shortcut too. A formula is a way of solving a particular problem.When figuring out the perimeter of a square, we can use this formula to help us.

P = 4s

Or

 P = s + s + s + s

Where P in the formula stands for perimeter and  stands for the measure of the side. Notice that in the first version of the formula we can take four and multiply it times the length of the side. Remember that multiplication is a shortcut for repeated addition. The second formula shows us the repeated addition. Either formula will work.

Let’s apply this formula to the square that we looked at with 5 ft on one side.

We can also use the formula with multiplication to get the same answer.

P = 4s

P = 4(5)

P = 20 ft

Rectangle:Arectangle has opposite sides that are congruent. In other words, the two lengths of the rectangle are the same length and the two widths of a rectangle are the same width. Let’s look at a diagram of a rectangle.

Notice that the side lengths have “next to them, this means inches. When we figure out the perimeter of the rectangle, we can’t use the same formula that we did when finding the perimeter of the square.A square has four sides of equal length. A rectangle has two equal lengths and two equal widths.

Now we can write the formula for the perimeter of a rectangle.

P = 2l + 2w

Since we have two lengths that have the same measure and two widths that have the same measure, then we can multiply two times one measure plus two times the other measure and that will give us the distance around the rectangle.

Ex: If we have a rectangle with a length of 8 inches and a width of 6 inches, we can substitute these measures into our formula and solve for the perimeter of the rectangle.

P = 2l + 2w

P = 2(8) + 2(6)

P = 16 + 12

P = 28 inches

Area of the 4 walls of a room :

If we look around and observe the walls of a room we find that generally the walls are in the shape of a rectangle the floor and the ceiling of the room are also of rectangular shape.

• ABCD, EFGH represent the floor and ceiling of the room.
• ABFE, BCGF, CDHG, DAEH represent the 4 walls.
• Area of floor = l × b;                        Area of roof =  l× b
•  Area of 4 walls = ABFE + BCGF + CDHG + DAEH

         =  lh + bh + lh + bh =  2lh + 2bh = 2h(l + b) =  2(l + b) × h = perimeter × height

•  Area of 4 walls =  p × h  square units.
•  If the floor of  a room is in the shape of a square.

          then we have l = b

          Area of 4 walls = 2h(l + b) = 2h(l + l) = (2h) × (2l)= 4lh sq. units.

perimeter,area,area and perimeter of a rectangle,rectangle,perimeter of rectangle,perimeter of a rectangle,area of rectangle,area and perimeter of rectangles,area and perimeter of a rectangle formula,area and perimeter of a rectangle and square,how to find area and perimeter of a rectangle,write a c program area and perimeter of rectangle