Sectors with equal area but different arcs

A sector has radius \(r\), angle \(\theta\) radians and arc length \(l\).

1. Show that the area of the sector is \(\dfrac{1}{2}rl\), and explain why this matches the area of a triangle with base \(l\) and height \(r\).[2]
2. A second sector has radius \(2r\) and angle \(\dfrac{\theta}{4}\). Compare its arc length and area with those of the first sector.[3]
3. A third sector has radius \(kr\), where \(k>0\), and the same area as the first. Find its angle in terms of \(\theta\) and \(k\), and its arc length in terms of \(l\) and \(k\).[2]