Show how we can use two identical copies of a trapezium to make a parallelogram. Class 9

Show how we can use two identical copies of a trapezium to make a parallelogram. Class 9

Question 1.

Show how we can use two identical copies of a trapezium to make a parallelogram. How will this give us the formula for the area of a trapezium? Class 9

Solution:

Take two identical trapeziums with parallel sides 'a' and 'b' and height 'h'.

Rotate one through 180°and join along the non-parallel sides.

∵ New figure formed is a parallelogram

Base of parallelogram = b + a = a + b, height = h

∵ Area of parallelogram = base × height

∴ Area of parallelogram = (a + b)h

∵ This parallelogram consists of two identical trapeziums

∴ 2 × Area of trapezium = (a + b)h

∴ Area of trapezium = $\frac{1}{2}$(a + b)h