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Q.

From a rectangular sheet of paper of size 100 cm × 80 cm, 4 squares, each of side 10 cm have been cut from each corner. Again, from the remaining piece of paper, an isosceles right triangle is removed whose equal sides are each of 10 cm length. So, the area of the remaining part of the paper is


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a

7550 m2

b

7232 m2

c

8711m2

d

7313 m2 

answer is A.

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Detailed Solution

Given as follows,
A rectangular sheet of paper of size  =100 cm × 80 cm
4 squares which are cut from corners have each side = 10 cm
An isosceles right triangle is removed whose equal sides have length  = 10 cm length.
We know that the area of the rectangle is the product of its length and breadth and the area of the triangle is on half of the products of its base and height.
Here, the area of the rectangle is,
 = 100 ×80=8000  cm 2
Again, the area of 4 square pieces that has been cut from the paper,
 = 4 × (10) 2  = 400 c m 2 . 
Next, the area of the isosceles triangle is,
=  1 2  ×base ×height =  1 2  ×10 ×10 = 50   cm 2
So, the final area of the remaining piece of paper is,
  A=Area rectangle −Area 4 squares −Area triangle =100×80−4× 10 2 − 1 2 ×10×10 =8000−400−50 =7550  cm 2
So, the area of the remaining part of the paper is obtained as 7550 cm 2 .
Hence, the correct option is 1.
 
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