Since the area of a parallelogram is , the area of a triangle must be
onehalf the area of a parallelogram. Thus, 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 in^{2})


= 30 in^{2}


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 cm^{2})


= 27 cm^{2}


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 in^{2})


= 20 in^{2}



Example 4:

The area of a triangularshaped 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 ft^{2} =·
(3 ft) ·


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


36 ft^{2} = (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

