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 cm^{2}.
Clearly,
the rectangle contains 3 rows of 5 squares. Therefore:
Area
= 5cm x 3cm
Area
= 15cm^{2}
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 = 200m^{2}
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:
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