The adjacent sides of a parallelogram measure 14 centimeters and 20 centimeters, and one angle measures 57°. Find the area of the parallelogram.

Verified Answer :

caylus

Hello,
Let's h the height of the parallelogram:
sin 57°=h/14==> h=11,741387...
Area=h*20=234,827759... (cm²)



The area of an isosceles triangle is given by

\(Area = base \: \times height\)
We have the base already given, so we just have to calculate the height using the sine ratio.

\(\sin(57 \degree) = \frac{h}{14}\)
\(\Rightarrow h = 14 \times \sin(57 \degree)\)

You may choose to use your calculator here, but I will prefer to keep it as it is and use the calculator value at the end.

Now let's plug our values inside the formula, yo obtain,

\(Area = 20 \times 14 \sin(57 \degree)\)
\(Area = 234.8 {cm}^{2}\)

\(Hence, the area of the parallelogram is 234.8cm²\)

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