Areas & Perimeters Part 2

Welcome to the second part of our Topic:-

# Area of rectangle:

Consider a rectangle of length 5 cm and width 3 cm.

Using the method of counting squares, we find that the area of the rectangle is 15 cm2.

Clearly, the rectangle contains 3 rows of 5 squares.  Therefore:

Area = 5cm x 3cm

Area = 15cm2
This suggests that:

The area of a rectangle is equal to its length multiplied by its width.  That is:

Area = Length x Width

Using the pro numerals A for area, l for length and w for width, we can write it simply as:

A = l x w

This is the formula for the area of a rectangle.

#### Example 1

Find the area of a rectangular field 20 m long and 10 m wide.

##### Solution:

A = lw

A=20m x 10m

Area of the field = 200m2

###### Note:

To find the area of a region enclosed within a plane figure, draw a diagram and write an appropriate formula.  Then substitute the given values and use a calculator, if necessary, to obtain the required area.

SQUARE:

A rectangle is a quadrilateral with four right angles and four equal sides, this defer from rectangle because only two opposite sides are equal.

# Perimeter of a square

Finding the perimeter of a square when a side is given and finding the length of a side when the perimeter is given are the goals of this lesson.

Given a square with side s, the perimeter (P) or distance around the outside of the square can be found by doing

P = s + s + s + s = 4 × s

Example 1:

Find the perimeter of a square when s = 3 cm

Solution:

P = 4 × s = 4 × 3 = 12 cm

Notice that it is perfectly ok to do P = 3 + 3 + 3 + 3 = 12

However, it is usually easier and quicker to do 4 times 3 than adding 3 four times

Example 2:

Find P when s = 5 cm

Solution:

P = 4 × s = 4 × 5 = 20 cm

Example 3:

Find perimeter of square with side = 2/8 cm.

Solution:

P = 4 × s = 4 × 1/8 = (4/1) × (2/8) = (4 × 2)/ ( 1 × 8 )= 8/8 = 1 cm

Example 4:

A square has a perimeter of 12 inches. Find its side

Solution:

Here, given the perimeter, you are asked to find the length of a side of the square.

We know that P = 4 × s

You should replace P by 12 because that is what they gave you.

So, 12 = 4 × s

The problem becomes a multiplication equation that you need to solve

However, you can solve this equation with mental math. Replace s by a question mark(?) and ask yourself the following:

4 times ? = 12 or 4 times what will give me 12? The answer is 3, so s = 3

The perimeter of a square is 64 cm. What is the length of one side?

Again, since P = 4 × s, we get 64 = 4 × s after replacing P by 64

Ask yourself 4 times what will give me 64? Since 4 times 16 is 64, s = 16

You don't have to guess 4 times what will give 64. You can also divide 64 by 4 to get 16

In fact, whenever you are looking for s and P is a big number, you should always divide p by 4 to get s

Notice that to get the perimeter of a rhombus, you can do the exact same thing we did above for the square.

Since just like the square, all sides of a rhombus are equal, there is absolutely no difference as far as getting the perimeter!

Therefore, P is also equal to s + s + s + s = 4 × s

Continue to the next page for the area of Square:-