ABC is a triangle with centroid 'O'. CF, AE and BD are medians of side AB, BC and CA. If ∠COE = 45°, and length of CF and AE are 18 cm and 24 cm, respectively, then find the area of the triangle ABC.
Show answer & explanation
Correct answer: B
Explanation
Given:
CF = 18 cm
AE = 24 cm
∠COE = 45°
O = Centroid
According to the formula:
Distance from centroid to vertex = (2/3) × median
Distance from centroid to side = (1/13) × median
OC = (2/3) × 18 = 12 cm
OE = (1/3) × 24 = 8 cm
Area of △COE = (1/2) × OC × OE × sin∠COE
Area of △COE = (1/2) × 12 × 8 × sin 45° = 24√2 cm²
Area of triangle ABC = 6 × Area of △COE
Area of triangle ABC = 6 × 24√2 = 144√2 cm²
Correct Answer: Option 2) 144√2 cm²