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

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

Answer 2

The area of an isosceles triangle is given by


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


`\sin(57 \degree) = (h)/(14)`

`\Rightarrow h = 14 * \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 * 14 \sin(57 \degree)`

`Area = 234.8 {cm}^(2)`


`<b>Hence, the area of the parallelogram is 234.8cm²</b>`