Explanation Formula: Area of a triangle with an inscribed circle: If P is the perimeter of the triangle and r is the length of radius of its inscribed circle, then the area A of the triangle is given by A = 1 2 r P Area of triangle: If a , b and c are lengths of sides of triangle, then area of triangle is given by the formula: A= s ( s - a ) ( s - b ) ( s - c ) Where s is the semi perimeter which is given by s = 1 2 ( a + b + c ) Area of circle: If r is the radius of circle, then area of circle is given by the formula: A c i r c l e = π r 2 Calculation: To find the area of inscribed circle, we have to find the radius of the circle. In order to find the radius of inscribed circle, we will use the following formula: A = 1 2 r P , Where A is the area of triangle, P is the perimeter of triangle and r is the radius of inscribed circle. The given triangle is an equilateral triangle with length of side 10 cm. The perimeter P of triangle is the sum of lengths of all sides. For an equilateral triangle, all sides are of equal length. That is, a = b = c = 10 Hence, perimeter P = 10 + 10 + 10 = 30 To find the area of triangle, let’s find the semi perimeter which is half of the perimeter of triangle. Thus, s = P 2 = 30 2 = 15 cm. Now, let’s find the area A of triangle. A = 15 ( 15 - 10 ) ( 15 - 10 ) ( 15 - 10 ) A = 15 × 5 × 5 × 5 A = 25 3 cm 2

Elementary Geometry for College Students

6th Edition

ISBN: 9781285195698

Author: Daniel C. Alexander, Geralyn M. Koeberlein

Publisher: Cengage Learning

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Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 8.5, Problem 28E

To determine

To find:

The area of circle inscribed in an equilateral triangle.

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Chapter 8.5, Problem 27E

Chapter 8.5, Problem 29E

Chapter 8 Solutions

Elementary Geometry for College Students

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