In the obtuse triangle DEF, side DE = 14 cm. Because angle DEF is obtuse, the perpendicular height from F to side DE meets the EXTENSION of DE outside the triangle, at a point G. The height FG = 8 cm. Side DF = 10 cm. What is the area of triangle DEF, in cm²?
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Worked Solution
Step 1: Identify the correct base–height pair. The base is DE = 14 cm. The matching perpendicular height is the one that is perpendicular to DE, which is FG = 8 cm. (DF = 10 cm is just a side of the triangle and is NOT perpendicular to DE.)
Step 2: It is fine that point G lies on the EXTENSION of DE outside the triangle. The area formula still uses the perpendicular distance from F to the line containing DE.
Step 3: Apply the formula: Area = ½ × base × height = ½ × 14 × 8.
Step 4: Compute: ½ × 14 = 7. Then 7 × 8 = 56.
Final answer: Area = 56 cm².
Answer: 56 cm²
Correct answer: 56 cm²
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