Question

find the area of a square if the measure of its each diagonal is 8cm​

Answer 1

Answer:

DIAGONAL OF A SQUARE=

$\sqrt{2} a$

$8cm = \sqrt{2} a \\ a = \frac{ \sqrt{2} }{8} \\ 0.1767766952966$

0.1767766952966 Cm^2

Answer 2

Answer: 32 cm^2

Step-by-step explanation:The relationship between the length d of one of the two congruent diagonals of a square and the length s of one of the 4 congruent sides of a square is given by the formula:

d = s√2 or, solving for s:

s = d/√2

The formula for the area A of a square is given by the formula:

A = s²

Substituting into the area formula for s, i.e., s = d/√2, we have:

A = (d/√2)²

= d²/(√2)² by a property of positive integral exponents.

= d²/[(√2)(√2)]

= d²/√4 by a property of radicals

= d²/2

Since we're given that d = 8 cm, then substituting into the area formula in terms of d, we get:

A = d²/2

= (8 cm)²/2

= [(8 cm)(8 cm)]/2

= 64 cm²/2

= (64/2) cm²

A = 32 cm² is the area of the given square.