Here is one of the ways to convert trapezium ABCD into a rectangle EFGH of equal area— Class 8

Here is one of the ways to convert trapezium ABCD into a rectangle EFGH of equal area— Class 8

Question 1.

Here is one of the ways to convert trapezium ABCD into a rectangle EFGH of equal area— Class 8

Given the trapezium ABCD, how do we find the vertices of the rectangle EFGH?

[Hint: If ∆AHI ≅ ∆DGI and ∆BEJ ≅ ∆CFJ, then the trapezium and rectangle have equal areas.]

Solution:

Find mid-points I and J of AD and BC respectively.

Through I and J, draw perpendiculars to DC meeting DC at G and F respectively and AB produced at H and E.

Then, EFGH is the required rectangle equal in area to trapezium.

Question 2.

Using the idea of converting a trapezium into a rectangle of equal area, and vice versa, construct a trapezium of area 144 cm². Class 8

Solution:

Construct a trapezium of parallel sides 18 cm and 14 cm, height 9 cm or of parallel sides 17 cm and 15 cm and height 9 cm.

Answer is not unique.