The problem asks to find the area $S$ of a sector with radius $r = 4$ and arc length $l = 10$.

1. Problem Description

The problem asks to find the area $S$ of a sector with radius $r = 4$ and arc length $l = 10$.

2. Solution Steps

The formula for the arc length $l$ of a sector with radius $r$ and central angle $\theta$ (in radians) is given by:

$l = r\theta$

The formula for the area $S$ of a sector with radius $r$ and central angle $\theta$ (in radians) is given by:

$S = \frac{1}{2}r^2\theta$

We can also express the area in terms of the arc length as:

$S = \frac{1}{2}rl$

Given $r = 4$ and $l = 10$, we can use the formula for the area $S$ in terms of $r$ and $l$:

$S = \frac{1}{2}rl = \frac{1}{2}(4)(10) = 20$

3. Final Answer

$S = 20$