13.5 Chapter summary

13.5 Chapter summary (EMA7V)

Presentation: 2GTH

• Area is the two dimensional space inside the boundary of a flat object. It is measured in square units.

• 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: \(\pi {r}^{2}\)

• A right prism is a geometric solid that has a polygon as its base and vertical sides perpendicular to the base. The base and top surface are the same shape and size. It is called a “right” prism because the angles between the base and sides are right angles.

• A triangular prism has a triangle as its base, a rectangular prism has a rectangle as its base, and a cube is a rectangular prism with all its sides of equal length. A cylinder is another type of right prism which has a circle as its base.

• 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. It is measured in cubic units.

• Volume formulae for prisms and cylinders:

  • 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.

• The triangular pyramid and square pyramid take their names from the shape of their base. We call a pyramid a “right pyramid” if the line between the apex and the centre of the base is perpendicular to the base. Cones are similar to pyramids except that their bases are circles instead of polygons. Spheres are solids that are perfectly round and look the same from any direction.

• Surface area formulae for right pyramids, right cones and spheres:

  • 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 for right pyramids, right cones and spheres:

  • 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: \(\frac{4}{3}\pi {r}^{3}\)

• Multiplying one or more dimensions of a prism or cylinder by a constant \(k\) affects the surface area and volume.