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 ΔPQR is:
Answer & explanation
Correct answer: option 3
Side of a triangle a = 8 cm
Area of triangle = \(\frac{\sqrt {3 }}{4}\) x \( {a }^{2 } \)
= Area of triangle ABC = \(\frac{\sqrt {3 }}{4}\) x 8 x 8 = 16\(\sqrt {3 }\)
As we know, if P, Q and R are the mid points of sides AB, BC and CA then,
Area of triangle PQR = \(\frac{1}{4}\) x Area of ABC
= Area of triangle PQR = \(\frac{1}{4}\) x 16\(\sqrt {3 }\) = 4\(\sqrt {3 }\) \( {cm }^{2 } \).