Question

Find the area of square where diagonal is 58√2 cm​

Answer 1

The area of square where diagonal is 58√2 cm​ = 3364 sq. cm

Given:

Length of diagonal of square = 58√2 cm

To find:

The area of this square

Solution:

Let the length of side of square be denoted by 'a' and the length of diagonal be denoted by 'd'.

d = 58√2 (Given)

Using pythagoras theorem, we can say

a^2 + a^2 = d^2

=> 2*(a^2) = d^2

=> a^2 = (d^2)/2

=> a = d/(2^(1/2))

Area of square is given as

A = a*a

  = a^2

  = (d/(2^(1/2)))^2

  = (d^2)/2

  = ((58√2)^2)/2

  = (58*58*2)/2

  = 3364 sq. cm

Hence,

area of square = 3364 sq. cm

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