find the area of the shaded region
Answers
Answer:
384 cm²
Step-by-step explanation:
Side AB =
√16² + 12²
= √256 + 144
= √400
= 20 cm
Area of shaded region = Area of whole triangle - Area of unshaded region
= 1/2 × 20 × 48 - 1/2 × 12 × 16
= 10 × 48 - 6 × 16
= 480 - 96
= 384 cm²
Step-by-step explanation:
In ∆ABD,
AD² + BD² = AB² [Pythagoras Theorem]
=> (12)² + (16)² = AB²
=> √(144 + 256) = AB
=> √400 = AB
=> AB = 20cm
Area of ∆ ABD = 1/2 × base × height
= 1/2 × 12 × 16 cm²
= 96 cm²
Semi- perimeter of ∆ABC (s)
= (52 + 48 + 20)/2 cm
= 120/2 cm
= 60 cm
Therefore, Area of ∆ ABC
=√{60 × (60 - 52) × (60 - 48) × (60 - 20)} cm²
= √ (60 × 8 × 12 × 40) cm²
= 480 cm²
Now, are of the shaded region = 480 - 96 cm²
= 384 cm²
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