http://www.ck12.org Chapter 10. Perimeter and Area
10.3 Area and Perimeter of Triangles
Here you’ll learn how to calculate the area and perimeter of a triangle and how the area of triangles relates to the
area of parallelograms.
What if you wanted to find the area of a triangle? How does this relate to the area of a parallelogram? After
completing this Concept, you’ll be able to answer questions like these.
Watch This
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Click image to the left for more content.CK-12 Foundation: Chapter10AreaandPerimeterofTrianglesA
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Click image to the left for more content.Brightstorm:Area ofTriangles
Guidance
If we take parallelogram and cut it in half, along a diagonal, we would have two congruent triangles. Therefore, the
formula for the area of a triangle is the same as the formula for area of a parallelogram, but cut in half.
Thearea of a triangleisA=^12 bhorA=bh 2. In the case that the triangle is a right triangle, then the height and base
would be the legs of the right triangle. If the triangle is an obtuse triangle, the altitude, or height, could be outside of
the triangle.
Example A
Find the area of the triangle.
This is an obtuse triangle. To find the area, we need to find the height of the triangle. We are given the two sides of
the small right triangle, where the hypotenuse is also the short side of the obtuse triangle. From these values, we see
that the height is 4 because this is a 3-4-5 right triangle. The area isA=^12 ( 4 )( 7 ) = 14 units^2.
Example B
Find the perimeter of the triangle from Example A.