# CBSE 9th Maths

## Areas Of Parallelograms And Triangles

### Area of a parallelogram

The area of a parallelogram is the product of any of its sides and the corresponding altitude.

Area of a parallelogram = b×h

Where b is the base and h is the corresponding altitude(Height).

### Area of a triangle

Area of a triangle = (1/2)×b×h

Where “b” is the base and “h” is the corresponding altitude.

## Theorems

### Parallelograms on the Common Base and Between the Same Parallels

Theorem: Parallelograms that lie on the common base and between the same parallels are said to have equal in area.

Two parallelograms are said to be on the common/same base and between the same parallels if
a) They have a common side.
b) The sides parallel to the common side lie on the same straight line.

### Triangles on the Common Base and Between the Same Parallels

Theorem: Triangles that lie on the same or the common base and also between the same parallels are said to have an equal area.
Here, ar(ΔABC)=ar(ΔABD)

Two triangles are said to be on the common base and between the same parallels if
a) They have a common side.
b) The vertices opposite the common side lie on a straight line parallel to the common side.

### Two Triangles Having the Common Base & Equal Areas

If two triangles have equal bases and are equal in area, then their corresponding altitudes are equal.

### A Parallelogram and a Triangle Between the Same parallels

Theorem: If a triangle and a parallelogram are on the common base and between the same parallels, then the area of the triangle is equal to half the area of the parallelogram.

A triangle and a parallelogram are said to be on the same base and between the same parallels if
a) They have a common side.
b) The vertices opposite the common side lie on a straight line parallel to the common side.