In wireless sensor networks (WSNs), area coverage is an important issue that aims to schedule a minimal number of sensors to cover the given monitoring area without any hole. Many of the existing strategies investigated that sensors are battery powered and considered Boolean Sensing Model (BSM). However, BSM affects the actual sensing quality since it did not consider the physical characteristics of the sensor. This study proposed an area coverage algorithm called <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit {MSQAC}$ </tex-math></inline-formula> , which considers the rechargeable sensors and utilizes solar-powered energy. The proposed mechanism aims to maximize the surveillance quality for a given monitoring area by applying the Probabilistic Sensing Model (PSM). Two issues have been investigated while designing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit {MSQAC}$ </tex-math></inline-formula> algorithm. The first one is the energy discharging rate of each sensor is larger than the energy recharging rate. Thus, how to better utilize the recharged energy by scheduling the right sensor in the right working time is a big challenge. The second challenge is the contribution of each sensor with or without cooperation is different by considering the PSM. If the neighboring sensors are scheduled at work in the same time slot, they can be treated as the combination set of neighboring sensors. It is another big challenge to find the best combination set of sensors for each space point at each time slot such that the minimal monitoring quality can be maximized. Through extensive simulations, it is shown that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit {MSQAC}$ </tex-math></inline-formula> yields the best performance in terms of monitoring quality ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit {QoM}$ </tex-math></inline-formula> ), coverage ratio and fairness index.