The adjacent sides of a parallelogram measure 14 centimeters and 20 centimeters, and one angle measures 57°. Find the area of the parallelogram.
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,
\(Area = 20 \times 14 \sin(57 \degree)\)
\(Area = 234.8 {cm}^{2}\)
\(Hence, the area of the parallelogram is 234.8cm²\)