What you will learn in Mensuration & Solid Geometry

1. 1. Perimeter and Area of Plane Figures

   Every area formula on the list is a rearrangement into a rectangle. None of them needs to be remembered separately.

2. 2. Triangle Area and Heron's Formula

   Three ways to find a triangle's area, and the real skill: knowing which one your measurements support.

3. 3. Circles, Arcs, Sectors and Segments

   Why the circle's area is pi r squared, where radians come from, and the difference between a sector and a segment.

4. 4. Nets, Plans, Elevations and Cross-Sections

   Flattening a solid, and slicing it. Both turn a three-dimensional object into something you can measure on paper.

5. 5. Surface Area of Prisms and Pyramids

   Walls that unroll into one rectangle, and four triangles that need the slant height rather than the vertical one.

6. 6. Cylinders, Cones and Spheres

   The one-third and the two-thirds, arrived at by pouring and by Cavalieri rather than by memory.

7. 7. The Frustum

   A cone with its tip removed — and every frustum formula is that sentence, written out.

8. 8. Composite Solids

   Volumes add. Surface areas do not — and this is where most of the marks in the topic are lost.

9. 9. Scaling: Length, Area and Volume

   Multiply every length by k, and areas go up by k squared while volumes go up by k cubed. The consequences are enormous.

10. 10. Seeing in Three Dimensions

    Plans and elevations throw information away, and Euler's relation is a pattern this module tests rather than proves.