Question

the area of a square ABCD is 36 cm sq. find the area of the square obtained by joining the midpoints of the sides of square ABCD​

Answer 1

Area of square = 1/2 the area of square obtained by joining the midpoints

Therefore the area of the square required= 36×1/2 =18 cm.sq

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Answer 2

$\large{\sf{\red{\underline{\underline{ItzRakhi20 \:here}}}}}$

Let ABCD be a square having an area of 36 cm².

Let P, Q , R , S be the midpoints of AB ,BC and DA respectively . Then , PQRS is a square ( given ).

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⠀Area of a square ABCD = 36cm²

Side of a square ABCD =

$\sqrt{36 cm = 6cm }$

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Hence , BQ = $\frac{1}{2} \times BC$$= ( \frac{1}{2} \times 6)$cm

$= 3$cm

⠀⠀⠀⠀BP = $\frac{1}{2} \times AB$$= ( \frac{1}{2} \times 6)$cm

$= 3$cm

From right triangle PBQ ,we have:

⠀⠀⠀PQ² = BP² + BQ²= ( 3²+3²)cm²⠀⠀⠀

⠀⠀⠀⠀⠀⠀= ( 9 + 9 )cm² = 18cm²

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$= >$$= \sqrt{18cm}$$= 3 \sqrt{2}cm$

So , Each side of the square PQRS $= 3 \sqrt{2}cm$

So , Area of the square PQRS

$(3 \sqrt{2²} )cm²$= 18 cm²

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