The area of a parallelogram with sides 3√2 and 4 cm is 12. Find the degree measure of the acute angle of the parallelogram.
Data: a – the smaller side of the given parallelogram (a = 3 * √2 cm), b – the large side (b = 4 cm); S – parallelogram area (S = 12 cm2).
To find the required measure of the acute angle of a given parallelogram, we will use the formula: S = a * b * sinφ, from where we can express: φ = arcsin (S / (a * b)).
Calculation: φ = arcsin (12 / (3 * √2 * 4)) = arcsin (1 / √2) = arcsin (√2 / 2) = 45º.
Answer: The acute angle of the given parallelogram should be equal to 45º.
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