Elementary Geometry for College St...
Solutions
Elementary Geometry for College St...
The length of the radius of a circle inscribed in an equilateral triangle is 7 in. Find the area of the triangle.
To find:
The area of the triangle.
Formula:
The area of an equilateral triangle (all sides congruent) can be found using the formula
Where s is the length of one side of the triangle.
Calculation:
Suppose a circle is inscribed in equilateral triangle. The radius of the circle is 7 in.
Sketch the circle in equilateral triangle:
The radius is the short side of a 30-60-90 triangle containing half of the base of the triangle and the apothem. Thus, we obtain:
a = 7
Half of the base of the triangle =
Since this is half of a side, we see that a whole side is
To find the area of an equilateral triangle:
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