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