mathschallenge.net logo

Circumscribed Triangle

Problem

An equilateral triangle is circumscribed.

Find the area of the triangle.


Solution

Consider the following diagram.

Using the Pythagorean Theorem, 4x2 = x2 + 9
therefore 3x2 = 9 implies x = radical3.

Area of triangle is 3radical3.

It can be seen that the perimeter of the triangle is 6radical3, i.e. double the area. What radius circle would have a circumscribed equilateral triangle with an area the same size as the perimeter?

Problem ID: 108 (Mar 2003)     Difficulty: 2 Star

Only Show Problem