Question

Analyze the diagram below and complete the instructions that follow. Find the area of QRS.
A. 202.9 square units
B. 215 square units
C. 238.7 square units
D. 273 square units

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,

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

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

$=238.7\text{sq.units}$