Solved Examples on Area

In this section we will discuss solved examples on area.
Area : The magnitude of the measurement of the region enclosed by a closed plane figure is called its Area .
For measuring areas of plane figures, we express their areas in terms of the areas of square whose side is of length 1 cm . We say that its area is 1 square centimeter and is written in short as 1 sq.cm or 1 cm
2 . This is standard unit of area.

Conversion of Units
Units of Length Units of Area
1) 1 cm = 10 mm 1) 1 cm2 = (10 x 10) mm2 = 100 mm2
2) 1 m = 10 dm 2) 1 m2 = (10 x 10) dm2= 100 dm2
3) 1 dm = 10 cm 3) 1 dm2 = (10 x 10) cm2 = 100 cm2
4) 1 m = 100 cm 4) 1 m2 = (100 x 100) cm2 = 10,000 cm2
5) 1 dam = 10 m 5) 1 dam2 = (10 x 10) m2 = 100 m2 = 1 acre
6) 1 hm = 100 m 6) 1 hm2= (100 x 100) m2 = 10,000 m2 = 1 hectare
7) 1 km = 10 hm 7) 1 km2 = ( 10 x 10) hm2 = 100 hm2
8) 1 km = 1000 m 8) 1 km2 = (1000 x 1000) m2 = 1,000,000 m2 = 100 hectare
There are different formulas to find the area of a regular 2D shapes.
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1) Find the area of rectangle, whose length is 6.4 cm and width is 5 cm.
Solution :
Area of rectangle = length x width
Area of rectangle = 6.4 x 5
⇒ = 32 cm
2
Area of rectangle = 32 cm
2
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2) Find the area, in hectare, of a field whose length is 240 m and width 110 m.
Solution :
Length = l = 240 m and width = w = 110 m
∴ Area of the field = l x w
⇒ = 240 x 110
= 26,400 m
2
= 26,400 / 10,000 [ Since 10,000 m
2 = 1 hectares ]
Area of field = 2.64 hectare
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3) A wall 4.84 m long and 3.1 m high is covered with rectangular tiles of size 22 cm by 10 cm. Find the total cost of the tiles at the rate of $1.50 per tile.
Solution :
Area of wall = length x height
= 4.84 x 3.1
= 15.004 m
2
= 15.004 x 10,000
= 150040 cm
2
Area of one tile = 22 x 10 = 220 cm
2
∴ Number of tiles = ( Area of the wall ) / ( area of 1 tile)
= 150040 / 220 = 682 tiles
Cost of 1 tile = $1.50
∴ Total cost = Number of tiles x cost of 1 tile
= 682 x 1.50
∴ Total cost = $ 1023
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solved examples on area :
4) Find the altitude of a parallelogram whose area is 2.25 m
2 and base is 25 dm.
Solution :
Area of parallelogram = 2.25 m
2
Base of parallelogram = 25 dm = 25 / 10 = 2.5 m
Area of Parallelogram = base x height ( altitude)
∴ Altitude = Area / base
= 2.25 / 2.5
∴ Altitude = 0.9 m.
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solved examples on area :
5) ABCD is a parallelogram, CM ⊥ AB and BL ⊥ AD.
If AB = 16 cm, AD = 12 cm and CM = 10 cm, find BL.
Solution :

AB = 16 cm and height CM = 10 cm>
∴ Area of parallelogram ABCD = base x height
= AB x CM
= 16 x 10
= 160 cm
2
Now, taking AD as a base,
Area of parallelogram ABCD = base x height
160 = AD x BL
160 = 12 x BL
∴ BL = 160 / 12
⇒ BL = 13.33 cm.

Mensuration : Area and Perimeter

Perimeter and Area of Irregular Shape
Area and Perimeter of the Rectangle
Area of Square (perimeter of square)
Perimeter and Area of Parallelogram
Perimeter and Area of Rhombus
Area of Trapezoid (Trapezium)
Perimeter and Area of Triangle
Herons Formula
Solved examples on Area

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