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| Area of a
Triangle Part I |
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Unit 1
>
Lesson 4 of 8 |
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The area of a
polygon
is the number of square units inside that polygon. Area is 2-dimensional like a carpet or an area rug. A triangle
is a three-sided polygon. We will look at several types of triangles in this lesson.
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![[IMAGE]](images/intro_triangle.gif)
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![[IMAGE]](images/parallelogram_triangle.gif) 
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To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a
parallelogram
can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.
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Since the area of a parallelogram is  , the area of a triangle must be
one-half the area of a parallelogram. Thus, the formula for the area of a triangle is:
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or |
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where  is the base, 
is the height and · means multiply.
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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.
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