9.
If the area of adjacent figure is 50 m², then find the length
and the breadth
2x
Answers
Rectangle
ABCD
LMNO
PQRS
Area
8 sq. cm
12 sq. cm
6 sq. cm
Length
4 cm
4 cm
2 cm
Breadth
2 cm
3 cm
3 cm
Length × Breadth
4 cm × 2 cm = 8 cm2
4 cm × 3 cm = 12 cm2
2 cm × 3 cm = 6 cm2
In each case we observe the length × breadth = Area of the rectangle.
Therefore, area of rectangle = length × breadth = l × b sq. units
From the above multiplication, we get the following facts:
Length of the rectangle = Area of the RectangleBreadth of the Rectangle
Breadth of the rectangle = Area of the RectangleLength of the Rectangle
Consider the following figures:
(i)
Area of a Rectangle
4Save
Area of each small square = 1 sq cm
Area of rectangle in figure 1 by counting the squares = 6 sq. cm
Area = 6 square cm
Length of rectangle = 3 cm
Breadth of rectangle = 2 cm
Area = 3 × 2 = 6 sq. cm
(ii)
Area of a Rectangle
4Save
Area of each small square = 1 sq cm
Area of rectangle in figure 2 by counting the squares = 10 sq. cm
Area = 10 square cm
Length of rectangle = 5 cm
Breadth of rectangle = 2 cm
Area = 5 × 2 = 10 sq. cm
Hence, area of rectangle = length × breadth
A = l × b where, A is the area, l and b are length and breadth of a rectangle.
Let us find the area of a rectangle having length 5 cm and breadth 4 cm.
Area of Rectangle
4Save
From the above figure, it is clear that we can divide this rectangle into 20 squares of sides 1 cm each. So, the area = 20 cm2
Thus the area of the rectangle = 5 cm × 4 cm
= 20 cm2
So when we multiply its length and breadth we get the area of the rectangle.
Solved examples to find the area of a rectangle when length and breadth are given:
1. Ron’s kitchen is 5 meter long and 3 meter broad. Find the area of the floor of the kitchen.
Solution:
Area = length × breadth
= 5 × 3
= 15 sq. m
2. Find the area of a rectangle of length 12 cm and breadth 3 cm.
Solution:
Length (l) of the rectangle = 12 cm.
Breadth (b) of the rectangle = 3 cm.
Area of the rectangle = length × breadth
= 12 × 3 sq cm.
= 36 sq cm.
3. Find the area of a rectangle of length 15 cm and breadth 6 cm.
Solution:
Length of the rectangle = 15 cm.
Breadth of the rectangle = 6 cm.
Area of the rectangle = l × b
= 15 × 6 sq cm.
= 90 sq cm.
4. Robert wants to paint the front wall of his house. The wall is 3 m long and 2.5 m broad. If the cost of painting is $ 120 per square metre, find the cost of painting the wall.
Solution:
Length of the wall = 3 m
Breadth of the wall = 2.5 m
Area of the wall = 3 × 2.5 sq. m
= 7.5 sq. m
The cost for per square metre painting is $ 120.
Therefore, the cost for 7.5 sq. m painting is $7.5 × 120 = $ 900
5. Find the area of a rectangle of length 17 cm and breadth 9 cm.
Solution:
The length of the rectangle = 17 cm.
the breadth of the rectangle = 9 cm.
The Area of the rectangle = l × b
= 17 × 9 sq cm.
= 153 sq cm.
6. A tennis court is 24 m long and 8 m broad. Find its area.
Solution:
The length of the tennis court = 24 m
The breadth of the tennis court = 8 m
Therefore, the area of the tennis court = 24 × 8 sq m.
= 192 sq. m
7. Find the area of a rectangle of length 24 mm and breadth 8 mm.
Solution:
Length of the rectangle = 24 mm.
Breadth of the rectangle = 8 mm.
Area of the rectangle = l × b
= 24 × 8 sq mm.
= 192 sq mm.
8. Find the area of a rectangle of length 37 mm and breadth 19 mm.
Solution:
Length of the rectangle = 37 mm.
Breadth of the rectangle = 19 mm.
Area of the rectangle = l × b
= 37 × 19 sq mm.
= 703 sq mm.
9. Mike has a rectangular garden of length 15 m and breadth 10 m. Her friend Adam has a square garden of side 12 m. whose garden is bigger and by how much?
Solution:
Length of Mike’s garden = 15 m
Breadth of Mike’s garden = 10 m
Area of Mike’s garden = 15 × 10 sq. m = 150 sq m
Area of Adam’s garden = 12 × 12 = 144 sq. m
Hence, Mike’s garden is bigger.
Questions and Answers on Area of a Rectangle:
Find the area of the given rectangles.
(i) Length = 4 cm, Breadth = 7 cm
(ii) Length = 15 cm, Breadth = 4 cm
(iii) Length = 4.2 m, Breadth = 50 cm
(iv) Length = 1 m 40 cm, Breadth = 5 m 50 cm
(v) Length = 65 mm, Breadth = 21 mm
Answers:
(i) 28 sq. cm
(ii) 60 sq. cm
(iii) 21,000 sq. cm
(iv) 7.7 sq. m
(v) 1365 sq. mm
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