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**Area of Triangles and Trapezoids**

Course 2 Area of Triangles and Trapezoids Warm Up Evaluate. 1 2 1. · 6 · 8 24 2. 1 2 · 5.4 · 7.2 19.44 3. 4(7 + 10) 68 ( ) 70.7

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**Area of Triangles and Trapezoids**

Course 2 Area of Triangles and Trapezoids Problem of the Day 4 in. 1.5 in. 7 in. An isosceles trapezoid has bases of 7 in. and 4 in. and height 1.5 in. Find its area by using only the formula for the area of a parallelogram. (5.5)(1.5) = 8.25 in2

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**Area of Triangles and Trapezoids Area of Triangles and Trapezoids**

Course 2 Area of Triangles and Trapezoids Area of Triangles and Trapezoids Learn to find the area of triangles and trapezoids.

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**Area of Triangles and Trapezoids**

Course 2 AF 3.1 Use variables in expressions describing geometric quantities. -Objective :Students will use variables in expressions describing geometric quantities for Areas of triangles and trapezoids by using equation formulas and scoring an 80% proficiency on an exit slip.

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**Area of Triangles and Trapezoids**

Course 2 Area of Triangles and Trapezoids A diagonal of a parallelogram divides the parallelogram into two congruent triangles. So the area of each triangle is half the area of the parallelogram. Height Height Base Base The base of a triangle can be any side. The height of a triangle is the perpendicular distance from the base to the opposite vertex.

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**Area of Triangles and Trapezoids**

Course 2 Area of Triangles and Trapezoids AREA OF A TRIANGLE The area A of a triangle is half the product of its base b and its height h. 1 2 A = bh h b

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**Additional Example 1A: Finding the Area of a Triangle**

Course 2 Areas of Triangles and Trapezoids Additional Example 1A: Finding the Area of a Triangle Find the area of the triangle. A. 1 2 A = bh Use the formula. 5 1 2 Substitute 8 for b and 5 for h. A = (8 · 5) 8 A = 20 The area of the triangle is 20 square units.

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**Additional Example 1B: Finding the area of a Triangle**

Course 2 Area of Triangles and Trapezoids Additional Example 1B: Finding the area of a Triangle Find the area of the triangle. B. 1 2 A = bh Use the formula. 12 1 2 A = (9 · 12) Substitute 9 for b and 12 for h. 9 A = 54 The area of the triangle is 54 square units.

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**Areas of Triangles and Trapezoids**

Course 2 Areas of Triangles and Trapezoids Try This: Example 1A Find the area of the triangle. A. 1 2 A = bh Use the formula. 1 2 Substitute 6 for b and 9 for h. A = (6 · 9) 9 A = 27 6 The area of the triangle is 27 square units.

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**Areas of Triangles and Trapezoids**

Course 2 Areas of Triangles and Trapezoids Try This: Example 1B Find the area of the triangle. B. 1 2 A = bh Use the formula. 1 2 Substitute 7 for b and 10 for h. 10 A = (7 · 10) A = 35 7 The area of the triangle is 35 square units.

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**Area of Triangles and Trapezoids**

Course 2 Area of Triangles and Trapezoids A parallelogram can be divided into two congruent trapezoids. The area of each trapezoid is one-half the area of the parallelogram. 1 2 Area of a trapezoid = (base of parallelogram)(height).

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**Area of Triangles and Trapezoids**

Course 2 Area of Triangles and Trapezoids The two parallel sides of a trapezoid are its bases. If we call the longer side b1 and the shorter side b2, then the base of the parallelogram is b1 + b2. 1 2 Area of a trapezoid = (base 1 + base 2)(height).

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**Area of Triangles and Trapezoids**

Course 2 Area of Triangles and Trapezoids AREA OF A TRAPEZOID b2 The area of a trapezoid is half its height multiplied by the sum of its two bases. 1 2 A = h(b1 + b2) h b1

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**Additional Example 2A: Finding the Area of a Trapezoid**

Course 2 Areas of Triangles and Trapezoids Additional Example 2A: Finding the Area of a Trapezoid Find the area of the trapezoid. A. 5 in. 1 2 A = h(b1 + b2) Use the formula. 1 2 A = · 6(5 + 9) 6 in. Substitute. 1 2 A = · 6(14) Add. 9 in. 84 A = 42 Multiply. The area of the trapezoid is 42 in2.

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**Additional Example 2B: Finding the Area of a Trapezoid**

Course 2 Areas of Triangles and Trapezoids Additional Example 2B: Finding the Area of a Trapezoid Find the area of the trapezoid. B. 1 2 12 cm A = h(b1 + b2) Use the formula. 1 2 A = · 7( ) 7 cm Substitute. 1 2 Add. A = · 7(28) 16 cm 196 A = 98 Multiply. The area of the trapezoid is 98 cm2.

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**Areas of Triangles and Trapezoids**

Course 2 Areas of Triangles and Trapezoids Try This: Example 2A Find the area of the trapezoid. A. 1 2 A = h(b1 + b2) Use the formula. 1 2 A = · 6(11 + 4) Substitute. 11 in. 4 in. 6 in. 1 2 · 6(15) Add. A = 90 A = 45 Multiply. The area of the trapezoid is 45 in2.

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**Areas of Triangles and Trapezoids**

Course 2 Areas of Triangles and Trapezoids Try This: Example 2B Find the area of the trapezoid. B. 1 2 A = h(b1 + b2) Use the formula. 16 cm 1 2 A = · 9(5 + 16) Substitute. 9 cm 1 2 · 9(21) Add. 5 cm A = 189 A = 94.5 Multiply. The area of the trapezoid is 94.5 cm2.

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**Area of Triangles Exploration Activity**

Cut out the pieces of the rectangle and the dotted rectangle and glue each piece on your notebook. 2) Use the ruler to find the sides of the rectangle and triangles in inches. (Find the Length and Width of the Rectangles and the Base and Height of Each triangle) 3) Once you have all the measurements, find the AREA for each shape! Use : A = L X W Use: (Base x Height) 1 2

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**Area of Triangles and Trapezoids Insert Lesson Title Here**

Course 2 Area of Triangles and Trapezoids Insert Lesson Title Here Lesson Exit Slip Find the area of each figure. 1. 3. 9 in2 2. 45 ft2 3 in. 9 ft 6 in. 10 ft 8 ft 10 ft 4. 87.5 ft2 60 ft2 7 ft 6 ft 15 ft 12 ft 4. What is the height of a triangle with area 36 cm2 and a base 9 cm? 8 cm

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