Intelligent reflecting surface (IRS) is a promising paradigm to reconfigure the wireless environment for enhanced communication coverage and quality. However, to compensate for the double pathloss effect, massive IRS elements are required, raising concerns on the scalability of cost and complexity. This paper introduces a new architecture of quasi-static IRS (QS-IRS), which tunes element phases via mechanical adjustment or manually re-arranging the array topology. QS-IRS relies on massive production/assembly of purely passive elements only, and thus is suitable for ultra low-cost and large-scale deployment to enhance long-term coverage. To achieve this end, an IRS-aided area coverage problem is formulated, which explicitly considers the element radiation pattern (ERP), with the newly introduced shape masks for the mainlobe, and the sidelobe constraints to reduce energy leakage. An alternating optimization (AO) algorithm based on the difference-of-convex (DC) and successive convex approximation (SCA) procedure is proposed, which achieves shaped beamforming with power gains close to that of the joint optimization algorithm, but with significantly reduced computational complexity.