Question

the diagonal of square field is 90cm .find its area

pls answer correct I'll mark brainliest
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Answer 1

Here we have to find out the area of a square.

The length of the diagonal is 90 cm

We will use this data to find out the side of the square

The relation between the side and diagonal of the square is

$diagonal = \sqrt{2}\times side\\side = \frac{diagonal}{\sqrt{2}} \\side = \frac{90}{\sqrt{2}}$

      = 63.64 cm

Now, area of square = side × side

                                  =   63.64 × 63.64

                                  = 4050.049 cm²

Hence, the area of the square will be 4050.049 cm²

Answer 2

Question

The diagonal of square field is 90 cm . Find its area.

Answer

$= \colorbox{azure}{ 4050} \sf \blue{cm}^{ \red2}$

Figure

$\begin{gathered} \sf{ \red{x \: cm }\:}\huge\boxed{ \begin{array}{cc} \: \: \: \: \: \sf\footnotesize{4050 \: cm^{2} }\\ \: \: \: \: \: \: \: \: \: \end{array}} \\ \: \: \: \: \: \sf{ \red{x \: c m}}\end{gathered}$

Solution

Let us suppose a diagonal is drawn inside the square field such that it measures to be 90 cm . Now , It will form a right angled triangle with its hypotenuse = 90 ; lest its perpendicular and base is identical say x cm for it is a square with all sides equal.

Now ,

Using Pythagoras Theorem,

H² = P² + B²

90² = x² + x²

8100 = 2x²

4050 = x²

Since , we have to calculate area of square

Area of Square = (side)²

Here , side = x cm

Area = x² = 4050 cm²

Area of Square = 4050 cm²

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Additional Information

Area of a square = Product of two diagonal ÷ 2

Measure for Diagonal = √2 × a

Moreover, Two diagonals of a square is identical

Thankyou