Question

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

Answer 1

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,

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

$Hence, the area of the parallelogram is 234.8cm²$

Answer 2

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