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An equilateral triangle is inscribed in a circle of radius 2r. express the area a within the circle but outside the triangle as a function of the length 3x of the side of the triangle.

Sagot :

The expression for the area within the circle but outside the triangle as a function of the length 3x of the side of the triangle is [tex]\frac{88r^2}{7}-\frac{9\sqrt{3} }{2}x^2[/tex].

It is given that:-

Radius of circle = 2r

Length of side of equilateral triangle = 3x

We have to find the expression for the area within the circle but outside the triangle as a function of the length 3x of the side of the triangle.

We know that,

Area of circle = [tex]\pi R^2[/tex]

Where R is the radius of the circle.

We have R = 2r

Area of an equilateral triangle = [tex]\frac{\sqrt{3} }{2}a^2[/tex]

Where, a is the length of side of equilateral triangle.

a = 3x

Hence,

Expression = [tex]\pi R^2-\frac{\sqrt{3} }{2}a^2[/tex]

Expression = [tex]\frac{22}{7}*(2r)^2-\frac{\sqrt{3} }{2}*(3x)^2 = \frac{88r^2}{7}-\frac{9\sqrt{3} }{2}x^2[/tex].

To learn more about area of an equilateral triangle, here:-

https://brainly.com/question/10681095

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