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Searching for ## Perimeter and Area of Polygons

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Algebra Foundations

You will derive the formulas for the area and perimeter of a triangle, and practice using these formulas.

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After completing this tutorial, you will be able to complete the following:

- Derive the formula of the perimeter of a triangle.
- Calculate the perimeter of a triangle.
- Derive the formula for area of a triangle.
- Calculate the area of a triangle by using base length and height.

Recall that the perimeter of a region is the length of the path that surrounds a region (or the sum of the lengths of the sides of the region), and that the area of this region is the number of square units covered by the region. Since the perimeter of any polygon is the sum of its side lengths, the perimeter of a triangle with side lengths a, b, and c is P=a+b+c.

The formula for the area of a triangle can be derived either from the formula for the area of a rectangle or from the formula for the area of a parallelogram. For the first derivation, consider a triangle drawn in a rectangle in the following way.

However, this right triangle was drawn so that the legs of the triangle coincide with two sides of the rectangle. What if the triangle was drawn in the rectangle in a different manner? For example, how much of the rectangle is taken up by the triangle below?

Approximate Time | 20 Minutes |

Pre-requisite Concepts | Students should know the formula for the area of a parallelogram, know the perimeter of a polygon, know the definition of a triangle and its properties, be able to calculate the distance between two points on the coordinate plane, and be familiar with the Pythagorean theorem. |

Course | Algebra Foundations |

Type of Tutorial | Concept Development |

Key Vocabulary | area, base, height |