Question

the length of a diagonal of a square is 8√2cm.find the length of its side and hence find the area of a square.

Answer 1

diagonal of a square =√2× side

=8√2=√2×side

side=8√2cm/√2

side=8cm

area of a square =side×side

=8cm×8cm=64Cm square

Answer 2

Given - Diagonal of square

Find - Length of side and area of square

Solution - The length of a side of square is 8 centimetres and the area of the square is 64 centimetres.

The diagonal of a square and the length of its side are related by the formula -

Diagonal = side*✓2

Now, Keep the values in the formula to find the side of length.

8✓2 = ✓2*side

Side = 8 centimetres.

Now, the area of the square is calculated by side².

Area of square = 8²

Area of square = 64 centimetres

Thus, the length of a side of the square is 8 centimetres and the area of the square is 64 centimetres.