Question

In the given figure (not drawn to scale), ABCD
and LMCN are rectangles. The dimensions shown
in the figure are in metres. If the perimeter of the
rectangle LMCN is 66 m, then find the area of the
shaded region.
options:-. 1. 124m² 2. 432m² 3. 160m². 4.284m²​

Answer 1

Step-by-step explanation:

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Answer 2

Area of shaded region is 160$(m^{2})$. Option 3 is correct.

Step-by-step explanation:

1. Given Data

   AB= DC= 12y

   BC= 9 y

   DN =7

   BM= y

   Perimeter of LMNC = 66 (m)

2. Rectangle ABCD

   Length of rectangle ABCD (L) = 12 y

   Width of rectangle ABCD (B) = 9 y

3. Rectangle LMNC

   Length of rectangle LMNC (l) = LM= DC- DN= 12y-7

   Width of rectangle LMNC (b) =MC= BC - BM= 9 y- y= 8 y

4. Perimeter of rectangle LMNC = 66

  2(l+b) =66

   So

   l+b=33

   12 y-7 +8 y =33

   20 y = 33+7

   20 y =40

   So

  y = 2

5.  Now

    Length of rectangle ABCD (L) = 12 y = 12×2= 24 (m)

   Width of rectangle ABCD (B) = 9 y =9×2= 18 (m)

   Length of rectangle LMNC (l) = 12y-7 = 12×2-7=17 (m)

   Width of rectangle LMNC (b) = 8 y =8×2=16 (m)

6. Area of shaded region =L×B-l×b

   Area of shaded region = 24×18-17×16

   Area of shaded region =160 $(m^{2})$