Geometry

Surface Area of Three-Dimensional Shapes

Surface Area of Three-Dimensional Shapes

Strategy for surface area: We find the total amount of wrapping paper needed to completely cover the shape e.g.

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Total surface area:

SA = 2 x (3 x 5) plus

2 x (4 x 5) plus

2 x (3 x 4)

SA = 2 x 15 + 2 x 20 + 2 x 12

SA = 30 + 40 + 24

SA = 94 m2

The total surface area of a cuboid can be generalised.

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Surface Area = 2 x (L x H) + 2 x (L x W) + 2 x (W x H)

Surface Area of a Cylinder

If the cylinder is ‘closed’ we consider the two ends and the lateral surface area:

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SA = ?r2 + ?r2 + ?d x L

SA = 2?r2 + ?dL imagine a label being cut from a tin of fruit. The label will be a rectangle (?d x L)

If the cylinder is ‘open’ we consider one end and the lateral surface area:

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SA = ?r2 + ?dL

Surface Area of a Triangular Prism

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SA =