Question

A square and an equilateral triangle of sides twice as long are cut and the pieces are rearranged to form a trapezium, as shown below:

If a side of the square is 2 cm, what are the perimeter and area of the trapezium?

Answer 1

Perimeter = 2 + 2\(\sqrt{3}\) + 2 + 2\(\sqrt{2}\) + 2\(\sqrt{3}\) + 2\(\sqrt{2}\)

= 4 + 4\(\sqrt{3}\) + 4\(\sqrt{2}\) = 4(1 + \(\sqrt{3}\) + \(\sqrt{2}\))

Area = 2² + \(\frac{1}{2}\) × 4 × 2\(\sqrt{3}\) = 4 + 4\(\sqrt{3}\)

= 4(1 + \(\sqrt{3}\)) = 4(1 + 1.73)

= 4 × 2.73 = 10.92 cm