A triangle has a perimeter of 28 cm and an inradius of 2.5 cm. What is its area?
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Answer: D. None of these
Explanation
The area of a triangle can be found by multiplying the semiperimeter by the inscribed circle radius. Dividing the perimeter of twenty-eight centimeters by two gives a semiperimeter of fourteen centimeters. Multiplying fourteen by the inradius of two point five results in an area of thirty-five square centimeters. The semiperimeter of a polygon is defined as exactly half of its total outer perimeter distance. The inradius is the radius of a circle drawn completely inside a polygon touching every single side. Specialized geometric formulas connect internal circle dimensions directly to the total enclosed area of triangles.
Option A suggests twenty-five square centimeters, which underestimates the product of the semiperimeter and inradius. Option B provides forty-two square centimeters, resulting from an incorrect arithmetic calculation of the formula components. Option C proposes forty-nine square centimeters, which exceeds the correct computed area value of thirty-five.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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