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 cm^{2} = (10 x 10) mm^{2} = 100 mm^{2} |
2) 1 m = 10 dm | 2) 1 m^{2} = (10 x 10) dm^{2}= 100 dm^{2} |
3) 1 dm = 10 cm | 3) 1 dm^{2} = (10 x 10) cm^{2} = 100 cm^{2} |
4) 1 m = 100 cm | 4) 1 m^{2} = (100 x 100) cm^{2} = 10,000 cm^{2} |
5) 1 dam = 10 m | 5) 1 dam^{2} = (10 x 10) m^{2} = 100 m^{2} = 1 acre |
6) 1 hm = 100 m | 6) 1 hm^{2}= (100 x 100) m^{2} = 10,000 m^{2} = 1 hectare |
7) 1 km = 10 hm | 7) 1 km^{2} = ( 10 x 10) hm^{2} = 100 hm^{2} |
8) 1 km = 1000 m | 8) 1 km^{2} = (1000 x 1000) m^{2} = 1,000,000 m^{2} = 100 hectare |
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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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