1Are all figures having equal area congruent? Explain with an example.
2Two figures match exactly when one is overlapped on the other. Are they congruent, and is their area equal?
3Quadrilaterals ABDC and ABFE both have AB as a side. C and D lie on a line parallel to AB, and E and F lie on a different line parallel to AB, closer to it. Are they formed on the same base and between the same parallel lines?
4Rectangle ABCD and triangle DEF are drawn so that A, E and B lie on one line and D, C and F lie on a line parallel to it. Name their bases. Do they stand on the same base? Do they lie between the same parallel lines?
5Lines ED and AB are parallel, with C between E and D. Segments EA, EB, AC and BD are drawn, and AC is parallel to BD. Identify the triangle and quadrilateral standing on the same base and lying between the same parallel lines.
6Parallelograms ABCD and ABEF stand on the base AB = 7 cm between the parallel lines AB and FC. The perpendicular DG from D to AB is 3 cm. Find the area of each parallelogram. What is the relation between them?
7Prove that parallelograms standing on the same base and lying between the same parallel lines are equal in area.
8AB ∥ XY. ABPQ is a rectangle and ABCD is a parallelogram, both with base AB and their other vertices on XY. Prove that the area of parallelogram ABCD = area of rectangle ABPQ.
9Why do all parallelograms standing between the same two parallel lines have the same height?
10Parallelogram ABCD has area 72 cm² and AB = 12 cm. Parallelogram ABEF stands on the same base AB between the same parallel lines. Find the area of ABEF and the distance between the parallel lines.
11Two parallelograms stand on the same base AB, but their top sides lie on two different lines parallel to AB. Are their areas equal? Give a reason.
12A rectangle and a parallelogram that is not a rectangle stand on the same base between the same parallel lines. Their areas are equal. Which of the two has the greater perimeter, and why?