# CLASS-9AREA OF A TRIANGLE

AREA OF TRIANGLE

1

Area of Triangle = ------- X Base X Corresponding Height

2 In any triangle , there are three sides. Any sides of the triangle may be taken as base and the length of perpendicular from the opposite vertex to the base is to considered as a corresponding height.

1

In given figure, area of ABC = (------- X BC X AD) sq. units

2

There are some examples are given below –

Example.1) Find the area of a triangle with base 36 cm and height 24 cm

1

Ans.) Area of the given triangle = ------- X Base X Height

2

1

= ------ X 36 X 24

2

=  18 X 24  =  432 cm²        (Ans.)

Example.2) The base of a any triangular field is 4 times of its altitude. If the cost of cultivating the field at  \$ 12 per hector is \$ 1536. Find its base & height.

Total Cost

Ans.)  Area of the Triangle  =  ---------------

Rate

1536

= --------- =  128 hectors

12

= (128 X 10000) m²   [ where, 1 hector = 10000 m² ]

=   1280000 m²

Let the altitude of the field be z meters, then the base of the triangle would be 4 z (as per the given condition)

1                          4z²

So, Area = (------ X 4z X z) m² = (-------) m² = 2 z² m²

2                           2

As per the given condition –

2 z² m² = 1280000 m²

Or,       z² =  640000

Or,       z  = √640000 = √800²

Or,       z  =  800

So, altitude = 800 m, and base = 4 z =  4 X 800

=  3200 m

Hence the required altitude is 800 m & base is 3200 m   (Ans.)