A ramp has a side wall whose top edge is the line y = 2x, with x and y in metres and 0 ≤ x ≤ 4…

Step 1. The exact area. The wall is a triangle with base $4$ metres and height $8$ metres, so its area is $\tfrac{1}{2} \times 4 \times 8 = 16$ square metres.

Step 2. The sum for $n$ strips. The width is $h = \dfrac{4}{n}$. The left-end heights are $0, 2h, 4h, \dots, 2(n-1)h$. Their sum is $2h \times \dfrac{n(n-1)}{2}$, so the strip sum is $h \times n(n-1)h = \dfrac{16(n-1)}{n} = 16 - \dfrac{16}{n}$.

Step 3. Eight strips. The sum is $16 - 2 = 14$ square metres and the error is $2$ square metres.

Step 4. The error below $0.4$. We need $\dfrac{16}{n} < 0.1$, so $n > 40$. At $n = 40$ the error is exactly $0.4$, which is not below it. The smallest whole number is $41$.