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Geometry

The formula for trapezoids' area is found using the area formulas for triangles and parallelograms.

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

- After completing this Activity Object, learners will be able to:
- Recognize that the area of a trapezoid is half the product of the sum of the bases and the height.
- Calculate the area of a trapezoid.

Area is the amount of square units of the interior region of a two-dimensional figure.

For example, to find the area of a square you would calculate the amount of square units of its interior region. You can find the area by counting the amount of squares inside the shape or can calculate the area by using a formula. Formulas vary according to the dimension of the polygon or shape.

Examples:

Knowing how to calculate the area of a triangle by using a formula can be helpful in finding the area of a trapezoid.

For example, to find the area of the following triangle, you would use the following formula: where b represents the base length and h represents the height.

To calculate the value of the area for this triangle, substitute the values for the variables as follows:

Therefore, the area for this triangle is

To calculate the area of a trapezoid you can divide the trapezoid into two triangles.

Cut the trapezoid into two triangles.

Use the formula for a triangle to find the area. Note that you will have to add the two areas together to determine the total area of the trapezoid.

Another way to find the area of trapezoid is to draw two trapezoids so that they create a parallelogram.

Draw a trapezoid and copy the exact trapezoid and turn it upside down. When you put them side by side, you will create a parallelogram.

Remember that the formula for a parallelogram is: A=bh, where b represents the base length and h represents the height.

As you can see, one trapezoid is half of the parallelogram, therefore the area can be calculated by: where a represents (base length)1, b represent (base length)2, and h represents the height.

The following key vocabulary terms will be used throughout this Activity Object:

- area - the number of square units of the inside of a two-dimensional shape or three-dimensional figure
- area of a parallelogram - A=bh (where b is the base length and h is the height of the parallelogram.)
- area of trapezoid - (where a and b are the bases and h is the height of the trapezoid.)
- area of a triangle - (where b is the base length and h is the height of the triangle.)
- formula - a general mathematical statement, equation, or rule
- height (h) - the perpendicular distance to the base
- parallelogram - a quadrilateral with two pairs of parallel and congruent sides
- polygon - a closed figure made by joining line segments, where each line segment intersects exactly two others
- trapezoid - a quadrilateral with one pair of parallel sides
- triangle - a polygon with three sides and three angles
- variable - a symbol or letter that stands for the value

Approximate Time | 25 Minutes |

Pre-requisite Concepts | Students should know the definitions of area, parallelogram, trapezoid, and triangle, and be able to calculate their areas. |

Course | Geometry |

Type of Tutorial | Visual Proof |

Key Vocabulary | area, trapezoid, triangle |