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 :
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e 4√3 cm2
In the ΔABC, point P, Q, R are mid points so,
Sides of the ΔPQR = 8/2 = 4 cm
s = (perimeter of the triangle PQR)/(2) = (4 + 4 + 4)/(2) = 6 cm
Area of PQR by Heron's formula,
= √(s(s - a)(s - b)(s - c))
= √(6(6 - 4)(6 - 4)(6 - 4))
= √(6(2)(2)(2)
= 4√3 cm2