find the area of a square whose diagonal is 8 cm
Answers
Answer:
16
Step-by-step explanation:
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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.