Math Geometry Problems, Online Education

 Problem 193. Area of a Triangle, Semiperimeter, Inradius

In the figure below, given a triangle ABC of area S, s is the semiperimeter (a + b + c) / 2, and r is the inradius.
Prove that S = s.r
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Elearning 193 Area of a triangle, inradius, semiperimeter
 

 

FACTS AND HINTS:

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."


1. AREA OF A TRIANGLE:

Proposition: The area of a triangle equals one-half the product of the length of a side and the length of the altitude to that side.

Triangle area base, altitude 

  

Home | Geometry | Search | Problems | 191-200 | Semiperimeter | Area of a Triangle | Email | By Antonio Gutierrez

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Last updated: Dec 2, 2014