1. The problem is to find the volume of a prismatoid using the prismatoid formula. 2. The prismatoid volume formula is: $$V = \frac{h}{6} (B_1 + 4B_m + B_2)$$ where $h$ is the height (distance between the two parallel bases), $B_1$ and $B_2$ are the areas of the two parallel bases, and $B_m$ is the area of the cross-section midway between the bases. 3. Important rules: - The bases must be parallel. - The cross-section area $B_m$ is taken exactly halfway between the bases. 4. To use the formula, first find the areas $B_1$, $B_2$, and $B_m$. 5. Then measure or find the height $h$ between the bases. 6. Substitute these values into the formula and simplify to find the volume. 7. This formula is useful because it approximates the volume of a solid with two parallel bases and varying cross-sections. 8. Example: If $B_1=10$, $B_2=14$, $B_m=12$, and $h=5$, then $$V = \frac{5}{6} (10 + 4 \times 12 + 14) = \frac{5}{6} (10 + 48 + 14) = \frac{5}{6} \times 72 = 60$$ 9. So the volume of the prismatoid is 60 cubic units. This method provides a straightforward way to calculate volumes of prismatoids.