1ABCD is a parallelogram with base AB = 8 cm. E is a point on line DC such that AE is perpendicular to AB and AE = 6 cm. Find the area of triangle ABE and of parallelogram ABCD, and find the relation between them.
2Prove that the area of a triangle is half of the area of a parallelogram standing on the same base and lying between the same parallels.
3E, F, G and H are the midpoints of the sides AB, BC, CD and DA of parallelogram ABCD. Prove that the area of parallelogram EFGH is half the area of parallelogram ABCD.
4A parallelogram has base 15 cm and height 8 cm. A triangle stands on the same base and lies between the same parallels. Find the area of the triangle.
5Triangle ABE and parallelogram ABCD stand on the same base AB = 6 cm and lie between the same parallels. The area of the triangle is 18 cm². Find the area of the parallelogram and the distance between the parallel lines.
6The third vertex of a triangle on base AB lies on the line DC extended beyond D, outside parallelogram ABCD. Is the triangle still half of the parallelogram? Give a reason.
7Explain why a diagonal divides a parallelogram into two triangles of equal area.
8Parallelogram ABCD has an area of 120 cm². E, F, G and H are the midpoints of AB, BC, CD and DA. Find the area of parallelogram EFGH and of triangle HEF.