In a triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12 cm and 9 cm, respectively. Then, the area of triangle ABC, in sq cm, is

Calculation:Draw a median from point CNow all THREE medians divide the Δ ABC into 6 triangles.⇒ Area of Δ ABC = 6 × Any small triangle that is formedPoint G is CENTROID,AG : GD = 2 : 1AD = 12 cm⇒ AG + GD = 12⇒ 3 = 12⇒ 1 = 12/3⇒ 1 = 4⇒ AG = 2 × 4 = 8 cm⇒ GD = 1 × 4 = 4 cmAlso BG : GE = 2 : 1,BE = 9 cm⇒ BG + GE = 9 cm⇒ 2 + 1 = 9 cm⇒ 3 = 9 cm⇒ 1 = 9/3⇒ 1 = 3⇒ BG = 2 × 3 = 6 cm⇒ GE = 1 × 3 = 3 cmNow, BE perpendicular to AD,In Δ BGD, ∠ BGD = 90° Area of Δ BGD = 1/2 × BG × GD⇒ Area of Δ BGD = 1/2 × 6 × 4⇒ Area of Δ BGD = 12 cm2Area of Δ ABC = 6 × Area of Δ BGD⇒ Area of Δ ABC = 6 × 12⇒ Area of Δ ABC = 72 cm2∴ The area of Δ ABC is 72 cm2. Median divide the triangle into 2 equal parts.The point of intersection of three medians is Centroid. A centroid divides each median in the RATIO 2 : 1 (vertex : base)