Question

Q9.
Area of a square is 16cm’. Find the area of the square joining the mid points of the sides.
एक वर्गाकार चतुर्भुज का क्षेत्रफल 16 सेमी है । उस वर्गाकार चतुर्भुज का क्षेत्रफल ज्ञात कीजिए जो कि दिये गये च
बिन्दुओं को जोड़कर बनाया गया हो।​

Answer 1

Let s be the side of the bigger square

$\implies \large {s \: }^{2} \: = 16 \: {cm} ^{2}$

$\implies \large \boxed{ s = 4 \: cm \:}$

Let the side of small square be a

Diagonal of small square = AD

$\implies \: a \sqrt{2} = 4$

$\implies \: \large{ a = \dfrac{4}{ \sqrt{2} } = \dfrac{2 \times 2}{ \sqrt{2} } }$

$\implies \: a \: = \dfrac{ \sqrt{2 } \times \sqrt{2} \times 2 }{ \sqrt{2} }$

Cancelling √2,

$\implies \boxed{ \large\: a = 2 \sqrt{2} \: cm }$

$\therefore \footnotesize{ the \: side \: of \: small \: square \: = 2 \sqrt{2} \: cm}$

Area of smaller square = a^2

$\implies \: area = {(2 \sqrt{2 \: )} \: }^{2} = 4 \times 2 = 8 \: cm \: ^{2}$

$\rightarrow \large \: Area \: of \: small \: square \: = 8 cm ^2$

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Area = 8 cm ^2

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hope it helps...