Chapter 6
Measuring Space: Perimeter and Area
CBSE Class 9
Mathematics Solutions
Educart Mathematics class Class 9 NCERT Exemplar cover
Question:

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?

Answer: Verified

Take two identical trapeziums and place one reversed beside the other.

A parallelogram is formed.

Base of parallelogram = a+ba + b

Height = hh

So,

Area of parallelogram =(a+b)h= (a + b)h

Since this parallelogram consists of two equal trapeziums,

Area of one trapezium =12(a+b)h= \frac{1}{2} (a + b)h

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(All Q's of this Chapter solved)
More NCERT Questions
Find the area of a quadrant of a circle whose circumference is 66 cm. Two rectangles have the same area and the same perimeter. Does this mean that they are congruent to each other? By dividing a trapezium into two triangles show that its area is, half the sum of the parallel sides multiplied by the height (the same formula as the one given above). You know that the area of a parallelogram is base × height. Using this and the figure, show that the area of a trapezium is half the sum of the parallel sides × height, i.e., 1/2 (a + b)h.