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Warm Up Evaluate.

Area of Triangles and Trapezoids. Course 2. Warm Up Evaluate. 1 2. 1. · 6 · 8. 24. 1 2. 2. · 5.4 · 7.2. 19.44. 3. 4(7 + 10). 68. 4. 3.5(12 + 8.2). 70.7. Area of Triangles and Trapezoids. Course 2. Problem of the Day. 4 in. 1.5 in. 7 in.

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Warm Up Evaluate.

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  1. Area of Triangles and Trapezoids Course 2 Warm Up Evaluate. 1 2 1. · 6 · 8 24 1 2 2. · 5.4 · 7.2 19.44 3. 4(7 + 10) 68 4. 3.5(12 + 8.2) 70.7

  2. Area of Triangles and Trapezoids Course 2 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

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

  4. 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.

  5. Area of Triangles and Trapezoids Course 2 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.

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

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

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

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

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

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

  12. Area of Triangles and Trapezoids Course 2 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 (base 1 + Area of a trapezoid = base 2)(height).

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

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

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

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

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

  18. 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 WUse: (Base x Height) 1 2

  19. Area of Triangles and Trapezoids Course 2 Insert Lesson Title Here Lesson Exit Slip Find the area of each figure. 1. 3. 9 in2 2. 3 in. 45 ft2 9 ft 6 in. 10 ft 10 ft 8 ft 4. 87.5 ft2 7 ft 60 ft2 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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