Question

1. what is the formula for the area of a segment?

$a_{segment}=a_{sector}-a_{lower\\ triangle}$
$a_{segment}=a_{circle}-a_{sector}$
$a_{segment}=a_{circle}-a_{lower\\ triangle}$
$a_{segment}=a_{lower\\ triangle}-a_{sector}$

Explanation:

A circular segment is the region bounded by a chord and the corresponding arc. Its area is calculated by taking the area of the sector (the "wedge" of the circle defined by the same arc and two radii) and subtracting the area of the isosceles triangle formed by the two radii and the chord.

Answer:

A. $A_{\text{segment}} = A_{\text{sector}} - A_{\text{lower triangle}}$