A map shows a lake. One unit on the map is 100 m…

Step 1. Meeting points. $\dfrac{y^2}{4} = \dfrac{y + 4}{2}$ gives $y^2 - 2y - 8 = 0$, so $y = -2$ or $y = 4$. The points are $(1, -2)$ and $(4, 4)$.

Step 2. Horizontal strips. Each strip runs from the parabola on the left to the line on the right. Its width is $\dfrac{y + 4}{2} - \dfrac{y^2}{4}$.

Step 3. The area. $\displaystyle\int_{-2}^{4} \left(\dfrac{y}{2} + 2 - \dfrac{y^2}{4}\right) dy = \left[\dfrac{y^2}{4} + 2y - \dfrac{y^3}{12}\right]_{-2}^{4} = \dfrac{20}{3} + \dfrac{7}{3} = 9$ square units.

Step 4. Hectares. One square unit is $10\,000\ \text{m}^2$, which is one hectare. So the lake covers $9$ hectares.

Step 5. Vertical strips. For $x$ from $0$ to $1$ the strip runs from the lower half of the parabola to the upper half. For $x$ from $1$ to $4$ the bottom is the line. That needs $2$ integrals, split at $x = 1$.