Question

The diagonal of a square 81 root 2 cm , find its area ?

Answer 1

Answer:

The length of a side is

9

c

m

. The length of the diagonal is

12.73

c

m

.

Explanation:

The formula for area of a square is:

s

2

=

A

where A=area and s=length of a side.

Hence:

s

2

=

81

s

=

√

81

Since

s

has to be a positive integer,

s

=

9

Since the diagonal of a square is the hypotenuse of a right-angled triangle formed by two adjacent sides, we can calculate the length of the diagonal using the Pythagorean Theorem:

d

2

=

s

2

+

s

2

where d=length of the diagonal and s=length of a side.

d

2

=

9

2

+

9

2

d

2

=

81

+

81

d

2

=

162

d

=

√

162

d

=

12.73

Answer 2

Answer:

Here is your answer mate,

Step-by-step explanation:

Question,

The diagonal of a square 81 root 2 cm , find its area ?

Answer,

Points that we should know

• Area of square is (side)²

• Diagonal = √2 × side

Solution,

Given,

Diagonal = 81 √2 cm

We know { diagonal = √2 side }

$side = \frac{diagonal}{ \sqrt{2} }$

$side \: = \frac{81 \sqrt{2} }{ \sqrt{2} }$

Side = 81cm

Now finding area of square,

Area = (side)²

Area = ( 81 ) ²

Area = 6561 cm²

So, area of square is 6561cm²

Have a good day ❤️