A square of side 5 centimetres and four isosceles triangles, each of one side 5 centimetres and the height to the opposite vertex 8 centimetres; these are to be joined to make a square pyramind. How much paper is needed for the job?

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Solution

Side of the square = 5 cm

Base of the isosceles triangle = 5 cm

Height of the isosceles triangle = 8 cm

Area of the square = (side)² = (5 cm)² = 25 cm²

Area of one isosceles triangle =

Area of four isosceles triangles = 20 × 4 cm² = 80 cm²

Area of the square pyramid = Area of the square + Area of four isosceles triangles

= (25 + 80) cm²

= 105 cm²

Thus, we need 105 cm² paper for the job.

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