# CBSE Class 9 Maths Areas of Parallelograms and Triangles

- Which of the following figures lie on the same base and between the same parallels? Write the common base and the two parallels.(I) (II)
- Prove that the area of a parallelogram is the product of any base of it and the corresponding altitude.
- ABCD is a quadrilateral and BD is one of its diagonals as shown in the figure. DC= 5 cm, Altitude=10 cm. Show that ABCD is a parallelogram. Find its area.
- Show that line segment joining the mid points of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms.
- If E, F, G and H are respectively the mid points of the sides of a parallelogram ABCD, show that ar(EFGH) = ar(ABCD).
- In the square ABCD of side 10 cm E and F are the mid points of AD and BC. Find the area of APE.
- In a parallelogram PQRS, Take a point A on RS and join P and Q. In how many parts, the parallelogram is divided? What are the shapes of these Parts? Divide the parallelogram into two parts of equal area.
- In a parallelogram ABCD, AB = 20 cm. The altitude corresponding to the side AB and AD are 14 cm and 10 cm respectively. Find AD.
- Prove that of all the parallelograms of the given sides, a rectangle has the greatest area.
- If each diagonal of a quadrilateral separates it into two triangles of equal area, then show that the quadrilateral is a parallelogram.