ABC is an equilateral triangle. P, Q and R are the mid-points of sides AB, BC and CA, respectively. If the length of the side of the triangle ABC is 11 cm, then find the area (in cm²) of triangle PQR.

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Step 1: Given ABC is an equilateral triangle with side length 11 cm.

Step 2: P, Q, and R are midpoints of sides AB, BC, and CA respectively.

Step 3: Triangle PQR formed by joining midpoints of the sides of triangle ABC is similar to ABC and its side length is half of ABC's side length.

Therefore, side of triangle PQR = 11/2 = 5.5 cm.

Step 4: Area of an equilateral triangle with side 'a' is given by (sqrt(3)/4) * a^2.

Step 5: Calculate area of ABC:
Area_ABC = (sqrt(3)/4) * 11^2 = (sqrt(3)/4) * 121 = (121 * sqrt(3))/4

Step 6: Area of PQR = (side of PQR / side of ABC)^2 * Area of ABC
= (5.5 / 11)^2 * (121 * sqrt(3))/4
= (1/2)^2 * (121 * sqrt(3))/4
= (1/4) * (121 * sqrt(3))/4
= (121 * sqrt(3))/16

Hence, the area of triangle PQR is (121√3)/16 cm².

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