A reduced planar body with area greater than $πΔ^2/4$

We construct a reduced planar convex body $R$ with thickness $\Delta(R)=1$ and $$\operatorname{area}(R)=0.786215\ldots>0.785398\ldots=\frac{\pi}{4}.$$ Thus $R$ is a counterexample to Lassak's conjectured upper bound $\operatorname{area}\le(\pi/4)\Delta^2$ for planar reduced bodies. The construction is given by an explicit support function, and the proofs use only elementary support-function, width, area, and contact-point computations.