- #1

Matt

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## Homework Statement

Find the circle segment area that has the boundaries of line segment AB and the minor arc ACB.

Give the area in an exact form in terms of surds and Pi. (see attachments for annotated picture & original question).

## Homework Equations

Equation 1: Area of a segment = Sector area - Triangle area

Equation 2: Sector area = Central angle/360 * pi * diameter

Equation 3: Triangle area = 0.5 * base * height

## The Attempt at a Solution

Area of sector = 120/360 * pi * 4

Simplified = 1/3 * pi/1 * 4/1 = 4/3 * pi [Units squared]

Area of one of the triangle = 0.5 * 1√3 * 1

Combined triangle area = 0.5 √3 x 2 = 1√3

Segment area = (4 * pi/3 - √3) [Units squared]

Approximated answer = 2.4567