Question

The area of a square ABCD is 36 cm2. Find the area of the square obtained by
joining the midpoints of the sides of the square ABCD.​

Answer 1

Answer:

18 cm^2

Step-by-step explanation:

For more details plz see the image attached with this one

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 ).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀

⠀Area of a square ABCD = 36cm²

Side of a square ABCD =

$\sqrt{36 cm = 6cm }$

⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀

⠀⠀⠀##Be brainly ☺️☺️✌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀

⠀$\huge\mathcal\color{teal}Hope\:it\:helps!!$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀