1On a square grid with diagonals, find and shade two parallelograms standing on the same base and lying between the same parallels, and show that they are equal in area.
2On the grid, find and shade a triangle that is equal to half the area of a parallelogram standing on the same base and lying between the same parallels.
3On the grid, find and shade a pair of triangles standing on the same base and lying between the same parallels, and show they are equal in area.
4Construct a parallelogram ABCD having AB = 4 cm, BC = 5.5 cm and ∠ABC = 60°. Then construct a parallelogram ABQP equal in area to ABCD having an angle of 120°.
5The area of parallelogram ABQP is equal to the area of parallelogram ABCD. How?
6Construct parallelogram ABCD with AB = 4 cm, BC = 5.5 cm and ∠ABC = 60°, and a parallelogram ABQP equal in area to it having one side 6 cm. Why are the areas of ABQP and ABCD equal?
7In the 120° construction, why must the arc cut from Q be exactly equal to AB?
8Parallelogram ABCD has AB = 4 cm and a height of about 4.763 cm. Could a parallelogram ABQP of equal area be drawn with AP = 4 cm? Give a reason.
9P is any point on the side DC of parallelogram ABCD, whose area is about 19.05 cm². Find the area of triangle APB.
10Construct a parallelogram ABCD with AB = 5 cm, AD = 4 cm and ∠DAB = 60°. Then construct a rectangle ABEF equal in area to it.