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Chapter 2: Q. 17 (page 120)

An equilateral triangle is inscribed in a circle

of radius r. See the figure in Problem 16. Express the area A within the circle, but outside the triangle, as a function of the length x of a side of the triangle.

Short Answer

Expert verified

The area within the circle, but outside the triangle, as a function of the length x of a side of the triangle is(蟺3-34)x2.

Step by step solution

01

Step 1. Find the area of the circle using r2=x23.

Area of the whole circle =蟺谤2=蟺(x23)

Area of the equilateral triangle with length of the sides, x=34x2.

02

Step 2. Subtract the area of equilateral triangle from the the area of the circle to find the required area.

So the area A within the circle, but outside the triangle, as a function of the length x of the side of the triangle is,

A=蟺虫23-34x2A=(蟺3-34)x2

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