Find the area of the shaded region in the following figure, where ABCD is a rectangle and all the corners are right-angled.

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872cm2

750 cm2

882 cm2

865 cm2

answer is C.

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Detailed Solution

We need to find the area of the shaded region.
Let’s name the corners of all the unshaded portions.

https://www.vedantu.com/question-sets/1a67f2b6-7830-4ecf-b23b-681ff051f2f52206678144094828560.png

We will start by finding the area of the horizontal strip.
The area of the rectangle:
= RS

\times

= 120 \times 3

= 360 c m^{2}

Now, we will find the area of two vertical stripes.
In rectangle MNVW,
NV = 90 cm.
MN = 3 cm.
Therefore, the area of rectangle

MNVW = 90 \times 3 = 270 c m^{2} .

We can see that the rectangle MNVW and the rectangle OQTU are of the same dimensions.
Therefore, the area of rectangle OQTU is

270 c m^{2}

.
Now that the stripes have intersected, we have a common area, which is calculated twice in the calculation of horizontal and vertical stripes. The overlapping area is of square EGHF and square IJKL.
Therefore, the side of the square is 3 cm.
Therefore, the area of square

EGHF = 3 \times 3 = 9 c m^{2}

Similarly, the area of IJKL is 9cm2 because both squares have the same dimensions.
By combining all of the horizontal and vertical strip areas and subtracting the overlapping section.
we get,