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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

Expectations: G1.2.2: Construct and justify arguments and solve multistep problems involving angle measure, side length, perimeter, and area of all types of triangles. G2.1.1: Know and demonstrate the relationships between the area formula of a triangle, the area formula of a parallelogram, and the area formula of a trapezoid. G2.1.2: Know and demonstrate the relationships between the area formulas of various quadrilaterals (e.g., explain how to find the area of a trapezoid based on the areas of parallelograms and triangles). 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

Anatomy of a Triangle Any side of a triangle can be the base of the triangle. An altitude of the triangle is a segment that is perpendicular to the line containing the base. There are 3 pairs of corresponding bases and altitudes for any triangle. The height of a triangle is the length of a particular altitude (relative to the length of a base). 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

Anatomy of a Triangle altitude base 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

altitude base 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

altitude base 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

Bases and Altitudes The base must be a side of the triangle, but the altitude does not have to be. In fact, the only triangles that have altitudes that are actual sides of the triangle are right triangles. 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**Area of a Right Triangle**

Use the area of a rectangle formula to justify the area of a right triangle formula. A = .5bh = .5ab 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

Area of Any Triangle If a triangle has a base of length b units and a height of h units, then the area of the triangle, A, is given by the formula: A = .5bh 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

Use either the area of a rectangle formula or the area formula for a right triangle to justify the area of a triangle formula. 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**Anatomy of a Parallelogram**

Any side of a parallelogram can be the base. The altitude of a parallelogram is a segment with its endpoints on the lines containing the bases, perpendicular to the bases. The height of the parallelogram is the length of the altitude. 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

base 2 altitude base 1 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

base 1 base 2 altitude 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**Area of a Parallelogram**

Using previous formulas, try to figure out the formula for the area of a parallelogram. 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**Area of a Parallelogram**

If a parallelogram has bases of b units and a height of h units, then its area, A, is given by the formula: 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

The parallel sides of a trapezoid are its bases. The nonparallel sides are the legs. A perpendicular segment from one base to the other is an altitude for the trapezoid. The length of the altitude is the height of the trapezoid 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

base 1 altitude leg leg base 2 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

Using known formulas, try to determine the formula for the area of a trapezoid. Be careful that you do not limit your formula to only isosceles trapezoids. 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

Area of a Trapezoid If a trapezoid has bases of b1 and b2 units and a height of h units, then the area, A, of the trapezoid is given by the formula: 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**Lengths are shown in inches on the drawing of the rectangle below**

Lengths are shown in inches on the drawing of the rectangle below. What is the shaded area, in square inches? 18 24 57 78 96 9 2 8 12 4/20/2017 5.1: Perimeter and Area

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

What is the area of a parallelogram with vertices at (0,0), (2,3), (5,0) and (7,3)? 10 14 15 21 35 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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**5.2: Areas of Triangles, Parallelograms and Trapezoids**

Assignment pages , #12, 15, 18, (all), 32, 36, 40, 44, 53 4/20/2017 5.2: Areas of Triangles, Parallelograms and Trapezoids

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