8-4 Area of Triangles and Trapezoids Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Lesson Review- “USE THE FORMULA” Find the area of each figure ft 2 Insert Lesson Title Here 84 ft 2 Course Area of Triangles and Trapezoids in or ft or

Warm Up Evaluate Course Area of Triangles and Trapezoids 1212 · 6 · · 5.4 · (7 + 10) ( )

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

Course Area of Triangles and Trapezoids AREA OF A TRIANGLE h b A = 1212 bh The area A of a triangle is half the product of its base b and its height h.

Find the area of the triangle. Additional Example 1A: Finding the Area of a Triangle Course Area of Triangles and Trapezoids 5 8 A = 1212 bh Use the formula. A = 1212 (8 · 5) Substitute 8 for b and 5 for h. A = 20 The area of the triangle is 20 square units.

Find the area of the triangle. Additional Example 1B: Finding the Area of a Triangle Course Area of Triangles and Trapezoids 9 A = 1212 bh Use the formula. A = 1212 (9 · 12) Substitute 9 for b and 12 for h. A = 54 The area of the triangle is 54 square units. 12

Find the area of the triangle. Course Area of Triangles and Trapezoids A = 1212 bh Use the formula. A = 1212 (6 · 9) Substitute 6 for b and 9 for h. A = 27 The area of the triangle is 27 square units. Check It Out: Example 1A 6 9

Find the area of the triangle. Course Area of Triangles and Trapezoids A = 1212 bh Use the formula. A = 1212 (7 · 10) Substitute 7 for b and 10 for h. A = 35 The area of the triangle is 35 square units. Check It Out: Example 1B 10 7

Course Area of Triangles and Trapezoids The two parallel sides of a trapezoid are its bases, b 1 and b 2. The height of a trapezoid is the perpendicular distance between the bases. h b1b1 b2b2

Course Area of Triangles and Trapezoids AREA OF A TRAPEZOID h b1b1 A = 1212 h(b 1 + b 2 ) The area of a trapezoid is half its height multiplied by the sum of its two bases. b2b2 In the term b 1, the number 1 is called a subscript. It is read as “b-one” or “b sub-one.” Reading Math

Find the area of the trapezoid. Additional Example 2A: Finding the Area of a Trapezoid Course Area of Triangles and Trapezoids 5 in. 6 in. 9 in. A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 6(5 + 9) A = 1212 · 6(14) A = 42 The area of the trapezoid is 42 in 2. Substitute. Multiply. Add.

Find the area of the trapezoid. Additional Example 2B: Finding the Area of a Trapezoid Course Area of Triangles and Trapezoids A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 7( ) A = 1212 · 7(28) A = 98 The area of the trapezoid is 98 cm 2. Substitute. Multiply. Add. 12 cm 16 cm 7 cm

Find the area of the trapezoid. Course Area of Triangles and Trapezoids A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 6(11 + 4) A = 1212 · 6(15) A = 45 The area of the trapezoid is 45 in 2. Substitute. Multiply. Add. Check It Out: Example 2A 4 in. 6 in. 11 in.

Find the area of the trapezoid. Course Area of Triangles and Trapezoids A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 9(5 + 16) A = 1212 · 9(21) A = 94.5 The area of the trapezoid is 94.5 cm 2. Substitute. Multiply. Add. Check It Out: Example 2B 16 cm 5 cm 9 cm

The state of Wisconsin is shaped somewhat like a trapezoid. What is the approximate area of the state? Additional Example 3: Geometry Application Course Area of Triangles and Trapezoids A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 300( ) A = 1212 · 300(373) A = 55,950 The area of Wisconsin is approximately 56,000 square miles. Substitute. Multiply. Add.

A large preserve has a similar trapezoid shape. What is the approximate area of the preserve? Check It Out: Example 3 Course Area of Triangles and Trapezoids 232 mi 116 mi A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 129( ) A = 1212 · 129(347) A = 22,446 The area of the preserve is approximately 22,446 square miles. Substitute. Multiply. Add. 129 mi

Lesson Quiz Find the area of each figure in 2 45 ft 2 Insert Lesson Title Here 60 ft ft 2 Course Area of Triangles and Trapezoids What is the height of a triangle with area 36 cm 2 and a base 9 cm? 8 cm