Question

Find the area of triangle PQR if PQ = QR = 12 and angle PQR = 120

Answer 1

Answer:

36√3 unit square

Step-by-step explanation:

A=1/2(ab)sin120

A=1/2(12*12) sin120

A=72*√3/2=36√3 unit square

Answer 2

The area of triangle PQR is 36√3 square units.

What is area?

The area can be defined as the space occupied by a flat shape or the surface of an object.

What is the formula for area of a triangle?

Area = (1/2) × base × height

According to the given question.

We have a triangle PQR.

In which PQ = QR and PQR = 120.

Draw a perpendicular bisector PM on RQ such that RM = QM = 6.

Now in triangle PQM we have

$sin120 = \frac{PM}{PQ}$

⇒$sin120 = \frac{PM}{12}$

⇒$\frac{\sqrt{3} }{2} =\frac{PM}{12}$

⇒ $PM = 6\sqrt{3}$

Now, the area of triangle PQR is given by

Area of PQR = 2 ×  area of triangle PQM

Area of PQR = 2 × $\frac{1}{2} (6)(6\sqrt{3} )$

Area of PQR = 36√3

Hence, the area of triangle PQR is 36√3 square units.

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