Question

The area of square is 144 sq cm. Let PQRS be the square obtained by joining the mid points of the side of square. Find perimeter and area of the square PQRS.

Answer 1

Answer:72 & 24sqrt2

Step-by-step explanation:

Well, since the area of the square is 144, the side length is 12. Thus, after connecting the midpoints, the side lengths of the of the smaller square is 6sqrt2. Thus, 6sqrt2 * 4 is 24sqrt2, which results in the area. As for the area, the area is simply 1/2 of the original square, which results in 72.

Answer 2

$\sf\large\red{\underline{ given : }}$

Area of 1st square ABCD is 144cm².

Side of 2nd square is 1cm greater than 1st square.

$\\ \sf\large\red{\underline{ to \: find : }}$

Area of 2nd square.

$\\ \sf\large\red{\underline{ to \: know : }}$

♣Area of square = side²

$\\ \sf\large\red{\underline{solution : }}$

We know ,

Area of 1st square ABCD is 144cm².

So, according to formula ,

$\sf\large\red{\underline{ }}144 = {side}^{2} \\ \\ \sf\large\red{\underline{ }}side \: = \sqrt{144} \\ \\ \sf\large\red{\underline{ }} = > side \: = 12cm$

We know , the 2nd square has the side 1cm more than 1st square .

∴ Side of 2nd square = 13cm

Area of 2nd square with side 13cm will be...

$\sf\large\red{\underline{ }}area \: = {side}^{2} \\ \\ \sf\large\red{\underline{ }}area \: = {13}^{2} \\ \\ \sf\large\green{\underline{ area \: = 169 {cm}^{2} }}$

∴ The answer is 169cm².