The area of a square field is $\frac{1}{4}$ hectare. Find the length of its diagonal in metres.

Given:

Area of square = $\frac{1}{4}$ hectare.

To do:

We have to find the length of its diagonal in metres.

Solution:

We know that,

1 hectare = 10000 sq m

$\frac{1}{4}$ hectare = $\frac{10000}{4}$ sq.m.  =  2500 sq.m.

Area of square = 2500 sq.m.

Area of a square = side $\times$ side

2500 = side $\times$ side

2500 = side² 

Side=√2500 

Side = 50 m

Length of the side of the square field = 50 m.

Diagonal of square = $\sqrt{50^{2} +50^{2}} =50\sqrt{2}$ m.

The length of the diagonal of the square field is $50\sqrt{2}$ m.

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Updated on: 10-Oct-2022

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