1Construct a triangle ABC in which AB = 4 cm, BC = 6.5 cm and \( \angle ABC = 120^\circ \). How can we construct a parallelogram having a side PB = 5 cm and equal in area to \( \triangle ABC \)?
2The area of the parallelogram PBDQ is equal to the area of \( \triangle ABC \). How?
3Construct a parallelogram ABCD in which AB = 5 cm, BC = 4 cm and \( \angle ABC = 60^\circ \). How can we construct a triangle PBE with a side PB = 6 cm and equal in area to the parallelogram ABCD?
4The area of the triangle PBE is equal to the area of the parallelogram ABCD. How?
5Why must D be the exact midpoint of BC and not any point on BC?
6A triangle has base 10 cm and height 6 cm. A parallelogram equal in area to it is to be drawn on half its base, between the same parallels. Find the base of the parallelogram and the area of both figures.
7A parallelogram has base 7 cm and height 4 cm. What base must a triangle between the same parallels have to be equal in area to it? Check the areas.
8In the construction of the parallelogram PBDQ, the height between ST and BC is about 3.5 cm. Could the question have asked for PB = 3 cm? Give a reason.
9Why is the line ST in the second construction parallel to BE, even though no angle was copied to draw it?