Triangle PQR is an obtuse triangle. QR = 14 cm is the base. Vertex P is positioned such that the perpendicular from P does not land inside the triangle — it falls on the extension of QR beyond R. The perpendicular distance from P to line QR (measured outside the triangle) is 6 cm. The slant side PQ measures 9 cm. What is the area of triangle PQR?
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Worked Solution
Step 1: Identify the base.
Base = QR = 14 cm.
Step 2: Identify the perpendicular height.
For an obtuse triangle, the perpendicular from the opposite vertex may fall outside the triangle, on an extension of the base line.
Here the perpendicular from P meets the extension of QR at 90°, and this perpendicular distance = 6 cm.
This 6 cm is the correct height regardless of where the foot of the perpendicular lands.
The slant side PQ = 9 cm is NOT the height.
Step 3: Apply the area formula.
Area of triangle PQR = ½ × base × height
= ½ × 14 × 6
= 42 cm²
Answer: 42 cm²
Correct answer: 42 cm²
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