Question

11. In the following figures, find the area of the shaded regions​

Answer 1

Answer:

fig.1)

Step-by-step explanation:

area of rectangle=18×10=180cm2

area of triangle ∆BCE=1/2×10×8=40cm2

area of triangle∆DEF=1/2 ×10×6=30cm2

area of shaded region=180-(40+30)

=180-70=110cm2 ans

Answer 2

Figure (i): Area of shaded region = 110 cm^2

Explanation: Length of rectangle (ABCD) = 18 cm, Breadth = 10 cm

Ar(ABCD) = L x B = 180 cm^2

Ar(ΔDEF) = 1/2 x DF x DE = 1/2 x 6 x 10 = 30 cm^2

Ar(ΔBEC) = 1/2 x EC x BC = 1/2 x 8 x 10 = 40 cm^2

Shaded Area = Ar(ABCD) - Ar(ΔDEF) - Ar(ΔBEC)

= 180 - 30 - 40 = 110 cm^2

Figure (ii): Area of shaded region = 150 cm^2

Explanation: Side of square (ABCD) = 20 cm

Ar(ABCD) = Side x Side = 400 cm^2

Ar(ΔCEB) = 1/2 x BE x CB = 1/2 x 20 x 10 = 100 cm^2

Similarly, Ar(ΔCDF) = 100 cm^2

Ar(ΔFAE) = 1/2 x AE x FA = 1/2 x 10 x 10 = 50 cm^2

Shaded Area = Ar(ABCD) - Ar(ΔCEB) - Ar(ΔCDF) - Ar(ΔFAE)

= 400 - 100 - 100 - 50 = 150 cm^2