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In Figure, ABCD is a square with AB = 15 cm. The area of the square BDFE is ____.

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Detailed Solution

The area of the square BDFE is 450

c m^{2} .

Given, ABCD is a square with AB = 15 cm.
Now, we can observe that the diagonal of the square ABCD is the side of the square BDEF.
Now, for a square with side length ‘a’, its diagonal is given as

2 × a

.
So, using the side length of the square ABCD, i.e., 15 cm, we have the side length of the square BDEF as,

= 2 × 15 = 152 c m

Now, the area of a square is the square of its side measure, so the area of the square BDEF will be,

= 1522 = 15 × 15 × 2 × 2 = 225 × 2 = 450 c m 2

Therefore, the area of the square BDEF is obtained as 450

c m 2

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