Question

Analyze the diagram below and complete the instructions that follow. Find the area of QRS.

Answer 1

Answer-

The area of QRS is 238.7 sq units.

Solution-

According to properties of supplementary angles,

$m\angle R+124=180\\\\m\angle Q+132=180$

So,

$\Rightarrow m\angle R=180-124=56,\ m\angle Q=180-132=48$

As the sum of measurement of all the angles in a triangle is 180, so

$\Rightarrow m\angle S+m\angle R+m\angle Q=180$

$\Rightarrow m\angle S=180-m\angle R-m\angle Q$

$\Rightarrow m\angle S=180-56-48=76$

Then the area of the triangle will be,

$\text{Area}=\dfrac{1}{2}qr\sin S$

$=\dfrac{1}{2}\times 21\times 23.43\times \sin 76$

$=238.7\text{sq.units}$