# Area of Rectangle

## Area of Rectangle

Area is the region covered by the plane figure. Rectangle is a four sided plane figure having its opposite sides equal and each angle 90°. Area of rectangle is measured by the product of its length and breadth.
Let ABCD be a rectangle and it is divided into unit squares of side 1cm each and hence the area of each square is 1 cm2.
Now,
Area of the rectangle ABCD = Total number of square boxes within rectangle.
= No. of squares along the length × No. of squares along the breadth
= 5 × 3
= 15
Since each square box have the area 1 cm2
Area of the rectangle ABCD = 15 × 1 cm2
= 15 cm2

Area of a rectangle = length (l)×breadth (b) = l×b

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Note:
Area is measured in square units. For example cm2, mm2, m2 etc. are the units of area.

### Workout Examples

Example 1: Find the area of the given rectangle.
Solution: Here,
Length of the rectangle (l) = 12cm
Breadth of the rectangle (b) = 6cm
Area of rectangle (A) = l × b
= 12cm × 6cm
= 72cm2

Example 2: Find the area of the given rectangle.
Solution: Here,
Length of the diagonal (d) = 13cm
Breadth of the rectangle (b) = 5cm
We know,
l2 + b2 = d2
or,          l2 + 52 = 132
or,          l2 + 25 = 169
or,          l2 = 169 – 25
or,          l2 = 144

Area of rectangle (A) = l × b
= 12cm × 5cm
= 60cm2

Example 3: If the length of a rectangle is double of its breadth and its perimeter is 30m, find its length, breadth and area.
Solution: Let,
Breadth of the rectangle (b) = x
Length of the rectangle (l) = 2x
Perimeter of the rectangle  = 30m
i.e.          2(l + b) = 30m
or,          2(2x + x) = 30
or,          2 × 3x = 30
or,          6x = 30
or,          x = 30/6
or,          x = 5m

Length of the rectangle (l) = 2x = 2 × 5m = 10m
Breadth of the rectangle (b) = x = 5m

Area of the rectangle = l × b
= 10m × 5m
= 50m2

Example 4: Find the area of the given combined figure.
Solution: Here,
Length of the rectangular surface (l) = 20m
Breadth of the rectanglular surface (b) = 14cm
Area of rectangular part (A1) = l × b
= 20cm × 14cm
= 280cm2
Again,
Base of triangular surface (b) = 14cm
Height of triangular surface (h) = 10cm

= 70cm2

Total area of the given figure = A1 + A2
= 280cm2 + 70cm2
= 350cm2

Example 5: Find the area of the shaded region given in the figure.
Solution: Here,
Length of the rectangle (l) = 24m
Breadth of the rectangle (b) = 14cm
Area of rectangle (A1) = l × b
= 24cm × 14cm
= 336cm2
Again,
Length of square (l) = 10cm
Area of triangular part (A2) = l2
= (10cm)2
= 100cm2
Area of the shaded region = A1 A2
= 336cm2 – 100cm2
= 236cm2

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#### 1 comment:

1. Some place mistake in solution ðŸ¤”ðŸ¤”ðŸ¤”