Question

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

Answer 1

Step-by-step explanation:

Your answer is 18 cm sq.

Let me show you the method of solving this problem…..

Area of the larger square is 36 cm sq. then the side of the square is 6 cm.

Now , if you join the midpoints of the sides of that square , then you’ll get another square , obviously smaller than the previous one .

Now, we can calculate the area of the new square in two ways.

First Method : Drawing the new square we get 4 triangles ,all identical, each with a right angle and the sides adjacent to the 90 degree angle equal 3cm.

Now, we can easily calculate the area of the 4 triangles .

Area of the new square

= area of the larger square - area of the 4 triangles

= 36 - 4*1/2*3*3 cm sq

=36 - 18 cm sq.

=18 cm sq.

Hence , 18 cm sq is your answer.

Answer 2

The area of the square obtained by joining the midpoints of the sides of the square ABCD is 9 cm².

Let's first a square ABCD with an area of 36 cm².

Let's label the midpoint of AB as E, the midpoint of BC as F, the midpoint of CD as G, and the midpoint of DA as H.

Now let's join the midpoints of the sides of square ABCD to form another square EFGH.

We can see that the side length of square EFGH is half the side length of square ABCD, because each side of square EFGH is made up of two adjacent midpoints of the sides of square ABCD.

Therefore, the area of square EFGH is:

Area(EFGH) = (Side length of EFGH)²

= (1/2 * Side length of ABCD)²

= (1/2 * √36)²

= 3²

= 9 cm²

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