In the given figure, all line segments of the shaded portion are of the same length and at right angles to each other. The same can be cut out of a board of side 10 cm. What is the area of the shaded portion ?

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Submitted by examrobotsa on

Q: 133 (IAS/2000)
In the given figure, all line segments of the shaded portion are of the same length and at right angles to each other. The same can be cut out of a board of side 10 cm. What is the area of the shaded portion ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,4,0,0,0,4,0

keywords: 

{'shaded portion': [0, 1, 0, 0], 'line segments': [0, 1, 0, 1], 'area': [0, 0, 0, 1], 'right angles': [1, 2, 2, 2], 'same length': [0, 1, 0, 2], 'figure': [0, 1, 1, 0], 'board': [0, 1, 2, 2], 'side': [1, 2, 1, 1]}

The correct answer is Option 3 which is 52 cm2.

Option 1 presents 36 cm2, which is the area you`d get by considering only 6 squares of side length 6 cm. This would mean you`re excluding two shaded squares, making this option incorrect.

Option 2 suggests an area of 48 cm2. This option would mean you`re considering only 8 squares, excluding one shaded square, which is incorrect.

Option 3 proposes an area of 52 cm2, which is the correct answer as it accounts for all 9 shaded squares (considering a square side length of 10 cm divided by 3, each unit square has an area of 52/9 cm2).

Option 4 indicates an area of 64 cm2 which would imply the presence of extra units we don`t have in the figure, thus, making it a wrong answer.