Q1 of 21 Page 72

Of four equal equilateral triangles, two are cut vertically into halves and two whole are put together to make a rectangle:


If a side of a triangle is 1 metre, what is the area and perimeter of the rectangle?


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


Breadth of the rectangle = Side of equilateral triangle = 1m


Length of rectangle = () = √3


Perimeter of rectangle = 1 + √3 + 1 + √3 = (2 + 2 √3) m


Area of rectangle = Length × Breadth


⇒ Area of rectangle = √3 × 1 = √3 m2


More from this chapter

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4

We have seen how we can draw a series of right triangles as in the picture.


i) What are the lengths of the sides of the tenth triangle?


ii) How much more is the perimeter of the tenth triangle than the perimeter of the ninth triangle?


iii) How do we write in algebra, the difference in perimeter of the nth triangle and that of the triangle just before it?

 5

What is the hypotenuse of the right triangle with perpendicular sides √2 centimetres and √3 centimetres? How much larger than the hypotenuse is the sum of the perpendicular side?

 2

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?


 3

Calculate the perimeter and area of the triangle in the picture.