Question

The area of a square ABCD
is 16cm^2.Find the area of square joining the mid point sides.

Answer 1

ignore the pic
bd=4√2
so sr=2√2
and hence area=8 cm²
for procedure refer to the pic. but the answer there is wrong

Answer 2

Area of square = side²
Let the side be x.
So, x²=16cm²
x=4cm.

Midpoint of the side divides the side in two equal parts.
So, side/2=4/2= 2cm.

The angles of the corner of the square are 90degrees.

So, In any of the corners of the square, a right-angled triangle has been formed, with base and perpendicular being the two half sides of the square, and the hypotenuse being the line which joins the midpoints.

So, base = perpendicular = 2cm

By Pythagoras theorem,

b²+ p²= h²
2²+2²= h²
4+4= h²
8=h²
h=2 root 2.

Since the hypotenuse is the side of the square formed after joining the midpoints, the area of that square will be h².

So the area of the square inside is 8cm ².

Hope it helped! Mark Brainliest if it did! Good luck! :)