how to find the area of the shaded region
AREA OF SHADED REGION
Example 1 :
Find the area of the shaded portion
Solution :
To find the area of shaded portion of given composite figure, first let us draw a line
Area of given figure = Area of ABGE + Area of GCFD
Area of ABGE :
Area of rectangle = Length⋅ Width
length BE = 6 m, width GE = 2 m
Area of ABGE = 6(2) = 12 m2
Area of GCFD :
Area of rectangle = Length ⋅ Width
length CD = 6 m, width FD = 2 m
Area of GCFD = 6(2) = 12 m2
Area of shadedportion = 12 + 12 = 24 m2
Example 2 :
Find the area of the shaded portion
Solution :
To find the area of shaded portion, we have to subtract area of GEHF from area of rectangle ABCD.
Area of shaded portion
= Area of rectangle ABCD - Area of square GEHF
Area of ABCD :
Area of rectangle = Length ⋅ Width
Length AB = 20 cm
Width AC = 16 cm
Area of ABCD = 20 (16) = 320 cm2
Area of GEHF :
Area of square (GEHF) = side ⋅ side
Length GE = 6 cm
Area of square GEHF = 6 ⋅ 6
Area of square (GEHF) = 36 cm2
Area of shaded region = 320 - 36 = 284 cm2
Example 3 :
Find the area of the shaded portion
Solution :
To find the area of shaded region, we have to subtract area of semicircle with diameter CB from area of semicircle with diameter AB and add the area of semicircle of diameter AC.
Area of shaded portion
= Area of AEB - Area of semicircle with diameter BC + area of semicircle with diameter AC
Area of semicircle AEB = (1/2) Πr2
= (1/2)⋅ (22/7)⋅ (14)2
= (1/2)⋅ (22/7)⋅ 14⋅ 14
= 22⋅ 14
= 308 cm2
Example 4 :
Find the area of the shaded region
Solution :
To find the area of shaded portion, we have to subtract area of semicircles of diameter AB and CD from the area of square ABCD.
Area of shaded portion
= Area of square ABCD - (Area of semicircle AEB + Area of semicircle DEC)
= a2 - [ (1/2) Πr2) + ((1/2) Πr2) ]
= 72 - Πr2
= 49 - (22/7)⋅ (7/2)2
= 49 - (22/7)⋅ (7/2) ⋅ (7/2)
= 49 - 38.5
= 10.5 cm2
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how to find the area of the shaded region
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