Question

how do I find the area of the wedge of a unit circle?

Answer 1

let the length of the arc be L

we know that in a circle if the length of the arc is l and radius is r and θ is the angle subtended (in radians) between the radii then θ = L/r

given that r = 1 unit ⇒ θ = L radians

we know that area of sector = πr² × θ/2π = (r²θ)/2

given r = 1 unit and θ = L radians

area of sector = (1² × L)/2 = L/2