In the given Square, XY is the line of symmetry. If AX=2cm. Find the area of the

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In the given Square, XY is the line of symmetry. If AX=2cm. Find the area of the figure.

Options:

A .

20 {cm}^{2}

B .

34 {cm}^{2}

C .

16 {cm}^{2}

D .

8 {cm}^{2}

Answer: Option C
:
C

The given figure is a square and $X Y$ is the line of symmetry.
Hence, $A X = B X = 2 c m .$
Therefore, $A B = A X + B X$
$= 2 c m + 2 c m$
$= 4 c m$
Since the length of one side is given we can determine its area enclosed by the formula Side x Side.
$∴$ The area of the square $= 4 \times 4$
$= 16 {cm}^{2}$

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