Q2 of 21 Page 72

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 a square is 2 centimetres, what are the area and perimeter of the trapezium?


First we find the sides of the equally cut triangles formed from the original equilateral triangle.


Slant height of trapezium = Diagonal of square = 2 √2 cm


Smaller side of trapezium = 2 √3 cm


Perimeter of trapezium = 2√2 + 2√3 + 2√2 + (2 + 2√3 + 2)


⇒ Perimeter of trapezium = (4√2 + 4√3 + 4) cm


Area of trapezium =


⇒ Area of trapezium =


⇒ Area of trapezium = (4√3 + 4) cm2


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