How do you find the area of this obtuse triangle?
Answers
Solution :
To find the area of ∆ABC , you can find the areas of ∆ADC and ∆CDB and then subtract the values.
Alternatively you can apply the sine rule
In triangle ADC
It's right angled
AC² = AD² + DC²
> 144 = (6+BD)² + 16
> (BD + 6)² = 128
> BD + 6 = |√128|
> BD = 8√2 - 6 units
AD = 6 + (8√2-6) = 8√2 units
Area of ∆ADC
> ½ × 8√2 × 4
> 16√2
Area of ∆BDC
> ½ × 4 × (8√2-6)
> 2(8√2-6)
> 16√2 - 12
Area of ∆ABC
>> 16√2 - (16√2-12)
>> 12 unit²
Answer : The area of the obtuse triangle ABC is 126 unit² .
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Step-by-step explanation:
Solution :
To find the area of ∆ABC , you can find the areas of ∆ADC and ∆CDB and then subtract the values.
Alternatively you can apply the sine rule
In triangle ADC
It's right angled
AC² = AD² + DC²
> 144 = (6+BD)² + 16
> (BD + 6)² = 128
> BD + 6 = |√128|
> BD = 8√2 - 6 units
AD = 6 + (8√2-6) = 8√2 units
Area of ∆ADC
> ½ × 8√2 × 4
> 16√2
Area of ∆BDC
> ½ × 4 × (8√2-6)
> 2(8√2-6)
> 16√2 - 12
Area of ∆ABC
>> 16√2 - (16√2-12)
>> 12 unit²
Answer : The area of the obtuse triangle ABC is 126 unit² .
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