Question 52
ABC is an equilateral triangle. P,Q and R are the midpoints of sides AB,BC and CA, respectively. If the length of the side of the triangle ABC is 8 cm, then the area of $$ \triangle PQR $$ is:
Solution
In the $$\triangle$$ ABC, point P, Q, R are mid points so,
Sides of the $$\triangle$$ PQR = 8/2 = 4 cm
s = $$\frac{perimeter of \triangle PQR}{2} = \frac{4 + 4 + 4}{2} = 6 cm
Area of $$\triangle$$ PQR by Heron's formula,
= $$\sqrt{s(s - a)(s - b)(s - c)}$$Â
=Â $$\sqrt{6(6 - 4)(6 - 4)(6 - 4)}$$
= $$\sqrt{6(2)(2)(2}$$
= 4$$\sqrt3 cm^2$$
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