Observe the shapes 1, 2, 3 and 4 in the figures. Which of the following statements is not correct?

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Shapes 1, 3 and 4 have different areas and different perimeters.

Shapes 1 and 4 have the same area as well as the same perimeter.

Shapes 1, 2 and 4 have the same area.

Shapes 1, 3 and 4 have the same perimeter.

answer is A.

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Detailed Solution

Given, a figure,
Question Image

Counting the number of lines for each of the four figures, we get the perimeters of the figures as follows,

P 1 = 22 units P 2 = 18 units P 3 = 22 units P 4 = 22 units

Next, counting the number of squares for each figure, we get the areas of the four figures as follows,

A 1 = 18 sq . units A 2 = 18 sq . units A 3 = 16 sq . units A 4 = 18 sq . units

Among the given statements, the statement in the first option states that the perimeter of the figure1, figure 3 and figure 4 have different areas and different perimeters.
But, as we calculated the areas and the perimeters, the perimeters of figure 1, figure 3 and figure 4 are the same i.e., 22 units.
Also, the areas of figure 1 and figure 4 are the same, i.e., 18 sq. units each, while that of figure 3 is 16 sq. units, which is different.
But as per the given statement, all the perimeters and areas for the figures 1, 3 and 4 should be different, which is not true.
So, it is clear that the statement in the first option is not in accordance with the results obtained.
Hence, the correct option is (1).

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