Triangle ABC has AB = 18 cm. The perpendicular height from C to AB is 12 cm. D is a point on AB such that AD : DB = 2 : 1. E is the midpoint of AC. Find the area of triangle BDE.
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Worked Solution
Step 1: Find BD.
AD : DB = 2 : 1 and AB = 18 cm
BD = 1/(2+1) × 18 = 1/3 × 18 = 6 cm
Step 2: Find the height from E perpendicular to AB.
E is the midpoint of AC, so E lies halfway along the side AC from A.
The height from E to line AB = ½ × (height from C to AB) = ½ × 12 = 6 cm
Step 3: Find the area of triangle BDE.
Base = BD = 6 cm, Height from E = 6 cm
Area = ½ × 6 × 6 = 18 cm²
Correct answer: 18 cm²
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