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```				   how how to find area of triangle
```

6 years ago

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```										Dear Nagendra

the formula for the area of a triangle is:

or

where  is the base,  is the height and · means multiply.

The base and height of a triangle must be  	perpendicular to each other.  In each of the examples below, the base is a side of  the triangle.  However, depending on the triangle, the height may or may  not  	be a side of the triangle.  For example, in the right triangle in  Example 2, the height is a side of the triangle since it is  	perpendicular to the base.  In the triangles in Examples 1 and 3, the  lateral sides are not perpendicular  	to the base, so a dotted line is drawn to represent the height.

Example 1:
Find the area of an  		acute triangle with a base of 15 inches and a height of 4 inches.

Solution:

=  · (15 in) · (4 in)

= · (60 in2)

= 30 in2

Example 2:
Find the area of a  		right triangle with a base of 6 centimeters and a height of 9 centimeters.

Solution:

= · (6 cm) · (9 cm)

= · (54 cm2)

= 27 cm2

Example 3:
Find the area of an  		obtuse triangle with a base of 5 inches and a height of 8 inches.

Solution:

= · (5 in) · (8 in)

= · (40 in2)

= 20 in2

Example 4:
The area of a triangular-shaped mat is 18 square feet and the base is 3 feet.  Find the height. 		(Note:  The triangle in the illustration to the right is NOT drawn to scale.)

Solution:
In this example, we are given the area of a triangle and one dimension, and we are asked to work  		backwards to find the other dimension.

18 ft2 =· (3 ft) ·

Multiplying both sides of the equation by 2, we get:

36 ft2 =  (3 ft) ·

Dividing both sides of the equation by 3 ft, we get:

12 ft =

Commuting this equation, we get:

= 12 ft

Summary:
Given the base and the height of a triangle, we can find the area.  Given the area  	and either the base or the height of a triangle, we can find the other dimension.   	The formula for area of a triangle is:

or

where  is the base,  is the height

All the best.
AKASH GOYAL

Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.
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```
6 years ago

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