7.5 Summary
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7.5 Summary (EMBJ5)
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Area is the two dimensional space inside the boundary of a flat object.
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Area formulae:
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square: \({s}^{2}\)
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rectangle: \(b\times h\)
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triangle: \(\frac{1}{2}b\times h\)
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trapezium: \(\frac{1}{2}\left(a+b\right)\times h\)
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parallelogram: \(b\times h\)
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circle: \(\pi {r}^{2}\)
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Surface area is the total area of the exposed or outer surfaces of a prism.
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A net is the unfolded “plan” of a solid.
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Volume is the three dimensional space occupied by an object, or the contents of an object.
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Volume of a rectangular prism: \(l\times b\times h\)
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Volume of a triangular prism: \(\left(\frac{1}{2}b\times h\right)\times H\)
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Volume of a square prism or cube: \({s}^{3}\)
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Volume of a cylinder: \(\pi {r}^{2}\times h\)
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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.
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Surface area formulae:
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square pyramid: \(b\left(b+2h\right)\)
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triangular pyramid: \(\frac{1}{2}b\left({h}_{b}+3{h}_{s}\right)\)
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right cone: \(\pi r\left(r+{h}_{s}\right)\)
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sphere: \(4\pi {r}^{2}\)
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Volume formulae:
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square pyramid: \(\frac{1}{3}\times {b}^{2}\times H\)
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triangular pyramid: \(\frac{1}{3}\times \frac{1}{2}bh\times H\)
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right cone: \(\frac{1}{3}\times \pi {r}^{2}\times H\)
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sphere: \(\frac{4}{3}\pi {r}^{3}\)
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