In Figure ABCD, find the area of the shaded region. D 8cm E 20 cm B F 10 cm 10 cm
Answers
Answer:
Here , the given figure ABCD is a square , whose each sides is 20 cm.
Area of shaded region = Area of the square - Area of the triangles i.e. ar[ EBF + EAF + CDE ]
Now ,
Area of the square = [ side ]^2
=> [ 20 ]^2
=> [ 20 ] * [ 20 ] = 400 cm^2
Hence , the area of square will be 400 cm^2
And ,
side [ DC = CB = AB = DA ] = 20 cm.
side [ AF = FB ] = 10 cm.
Then , side will be AE = AD - DE
AE = 20 - 8 = 12
Hence , the side AE = 12 cm.
Since two sides of a right triangle are perpendicular then one of the perpendicular side will be height and other will be base of a triangle.
Then , area of the will be ,
According to the question ;
=> 400 - [ 1 / 2 * 10 × 20 ] + [ 1 / 2 * 10 × 12 ] + [ 1 / 2 * 8 × 20 ]
=> 400 - [ 100 ] + [ 60 ] + [ 80 ]
=> 400 - 240
=> 160 cm^2
Hence , the area of shaded region is 160 cm^2.
please brainliest mark
Answer:
160cm^2
Step-by-step explanation:
Required area of shaded region:
Area of square (ABCD) – Sum of areas of three triangles (AEF + BCF + DEC) _________ (1)
From the figure,
AB = BC = CD = DA = 20 cm allsidesofsquareisequal
AF = FB = 10 cm Given
Calculating area of square ABCD :
Side of square (a) = 20 cm
Area of square (a2)
= (20)2
= 400
Therefore, the area of square is 400 cm2
Calculating area of the 3 triangles :
i) ar(△AEF) = 12×b×h
= 12×AF×AE
AF = 10 cm (Given)
AE = 12 cm 20(AD)–8(ED)andAE=AD−ED
Substituting:
= 12×10×12
= 60
Therefore, the area of triangle AEF is 60cm2.
ii) ar(△BCF)= 12×b×h
= 12×BF×CB
BF = 10 cm
CB = 20 cm
Substituting:
= 12×10×20
= 100
Therefore, the area of triangle BCF is 100cm2
iii) ar(△DEC)= 12×b×h
= 12×DC×DE
DC = 20 cm
DE = 8 cm
Substituting:
= 12×20×8
= 80
Therefore, the area of triangle DEC is 80cm2
Substituting the obtained values in (1), we get:
Area of square (ABCD) – Sum of areas of three triangles (AEF + BCF + DEC)
400 – (100 + 60 + 80)
400 – 240 = 160
Therefore, the required area of the shaded region is calculated to be 160cm2.