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If the inradius of a triangle with perimeter 32 cm is 6 cm, then the area of the triangle (in sq. cm) is (SSC CGL 1st Sit. 2013)
- a)48
- b)100
- c)64
- d)96
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If the inradius of a triangle with perimeter 32 cm is 6 cm, then the a...
Area of triangle = Inradius × Semi-perimeter
= 6 ×16 = 96 sq. cm.
= 6 ×16 = 96 sq. cm.
Most Upvoted Answer
If the inradius of a triangle with perimeter 32 cm is 6 cm, then the a...
Area of triangle = Inradius × Semi-perimeter
= 6 ×16 = 96 sq. cm.
= 6 ×16 = 96 sq. cm.
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Community Answer
If the inradius of a triangle with perimeter 32 cm is 6 cm, then the a...
Understanding the Problem
The problem gives us the perimeter and inradius of a triangle and asks us to find the area.
Given Data
- Perimeter (P) = 32 cm
- Inradius (r) = 6 cm
Formula for Area of a Triangle
The area (A) of a triangle can be calculated using the formula:
\[ A = r \times s \]
where:
- \( r \) is the inradius,
- \( s \) is the semi-perimeter.
Calculating the Semi-Perimeter
To find the semi-perimeter (s):
\[ s = \frac{P}{2} \]
Substituting the given perimeter:
\[ s = \frac{32}{2} = 16 \, \text{cm} \]
Calculating the Area
Now, using the area formula:
\[ A = r \times s \]
Substituting the values of \( r \) and \( s \):
\[ A = 6 \, \text{cm} \times 16 \, \text{cm} \]
\[ A = 96 \, \text{cm}^2 \]
Final Answer
Thus, the area of the triangle is \( 96 \, \text{cm}^2 \).
The correct answer is option 'D'.
The problem gives us the perimeter and inradius of a triangle and asks us to find the area.
Given Data
- Perimeter (P) = 32 cm
- Inradius (r) = 6 cm
Formula for Area of a Triangle
The area (A) of a triangle can be calculated using the formula:
\[ A = r \times s \]
where:
- \( r \) is the inradius,
- \( s \) is the semi-perimeter.
Calculating the Semi-Perimeter
To find the semi-perimeter (s):
\[ s = \frac{P}{2} \]
Substituting the given perimeter:
\[ s = \frac{32}{2} = 16 \, \text{cm} \]
Calculating the Area
Now, using the area formula:
\[ A = r \times s \]
Substituting the values of \( r \) and \( s \):
\[ A = 6 \, \text{cm} \times 16 \, \text{cm} \]
\[ A = 96 \, \text{cm}^2 \]
Final Answer
Thus, the area of the triangle is \( 96 \, \text{cm}^2 \).
The correct answer is option 'D'.
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If the inradius of a triangle with perimeter 32 cm is 6 cm, then the area of the triangle (in sq. cm) is (SSC CGL 1st Sit. 2013)a)48b)100c)64d)96Correct answer is option 'D'. Can you explain this answer?
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