Rectangle ABCD has AB = 20 cm and BC = 12 cm. Point P lies on AB such that AP = 8 cm. Find the area of triangle PCD.
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Worked Solution
Step 1: Find the area of rectangle ABCD.
Area = AB × BC = 20 × 12 = 240 cm²
Step 2: Find PB.
PB = AB − AP = 20 − 8 = 12 cm
Step 3: Find the area of triangle APD.
Base = AP = 8 cm, Height = AD = BC = 12 cm
Area = ½ × 8 × 12 = 48 cm²
Step 4: Find the area of triangle PCB.
Base = PB = 12 cm, Height = BC = 12 cm
Area = ½ × 12 × 12 = 72 cm²
Step 5: Find the area of triangle PCD by subtracting the two surrounding triangles from the rectangle.
Area of △PCD = 240 − 48 − 72 = 120 cm²
Correct answer: 120 cm²
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