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What is the area of the circle (approximately) inscribed in a triangle with side lengths 12 cm, 16 cm and 20 cm ?
48 square cm
50 square cm
52 square cm
54 square cm
To find the area of the incircle of a triangle, we can use the formula:
Area=r×s
where r is the inradius and s is the semi-perimeter. The semi-perimeter s is calculated as 12+16+202=24 cm.
The area A for a triangle with sides 12 cm, 16 cm, and 20 cm can be found using Heron's formula:
A=s(s−a)(s−b)(s−c)=24×(24−12)×(24−16)×(24−20)
A=24×12×8×4=9216=96 square cm
The inradius r is given by:
r=As=9624=4 cm
Thus, the area of the incircle is:
Area=πr2=π×42≈50 square cm
- Option 1: 48 square cm - This is too low.
- Option 2: 50 square cm -
- Option 3: 52 square cm - This is too high.
- Option 4: 54 square cm - This is also too high.
Correct Answer: Option 2 - 50 square cm
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