7.5 Summary

7.5 Summary (EMBJ5)

• Area is the two dimensional space inside the boundary of a flat object.

• Area formulae:

  • square: \({s}^{2}\)

  • rectangle: \(b\times h\)

  • triangle: \(\frac{1}{2}b\times h\)

  • trapezium: \(\frac{1}{2}\left(a+b\right)\times h\)

  • parallelogram: \(b\times h\)

  • circle: \(\pi {r}^{2}\)

• Surface area is the total area of the exposed or outer surfaces of a prism.

• A net is the unfolded “plan” of a solid.

• Volume is the three dimensional space occupied by an object, or the contents of an object.

  • Volume of a rectangular prism: \(l\times b\times h\)

  • Volume of a triangular prism: \(\left(\frac{1}{2}b\times h\right)\times H\)

  • Volume of a square prism or cube: \({s}^{3}\)

  • Volume of a cylinder: \(\pi {r}^{2}\times h\)

• A pyramid is a geometric solid that has a polygon as its base and sides that converge at a point called the apex. The sides are not perpendicular to the base.

• Surface area formulae:

  • square pyramid: \(b\left(b+2h\right)\)

  • triangular pyramid: \(\frac{1}{2}b\left({h}_{b}+3{h}_{s}\right)\)

  • right cone: \(\pi r\left(r+{h}_{s}\right)\)

  • sphere: \(4\pi {r}^{2}\)

• Volume formulae:

  • square pyramid: \(\frac{1}{3}\times {b}^{2}\times H\)

  • triangular pyramid: \(\frac{1}{3}\times \frac{1}{2}bh\times H\)

  • right cone: \(\frac{1}{3}\times \pi {r}^{2}\times H\)

  • sphere: \(\frac{4}{3}\pi {r}^{3}\)