The obtuse angle of the rhombus is 150 ° and its side is 12 cm, find the area of the rhombus.

Given: ABCD – rhombus;

AB = 12 cm;

<B = 150 °;

Find: SABCD -? cm ^ 2.

The area of a rhombus is found by the formula:

SABCD = a ^ 2 * sina.

You can reason like this:

If a is an acute angle of a rhombus, then we find it as follows:

<B = <D = 150 °;

<A + <C = 360 ° – 150 ° * 2 = 360 ° – 300 ° = 60 °;

<A = <C = 60 °: 2 = 30 °.

sin30 ° = 1/2.

So SABCD = 12 ^ 2 * 1/2 = 144 * 1/2 = 72 (cm ^ 2).

Or like this:

If a is an obtuse angle of a rhombus, then:

In this formula for finding the area, in fact, it does not matter which sine of which angle to find, since the sine of an obtuse angle is sin (p – a) = sina. Those. sin (p – a) = sin (180 ° – 150 °) = sin30 °.

The area of the rhombus is calculated in the same way.

Answer: the area of the rhombus is 72 cm ^ 2.