Holt CA Course Area of Triangles and Trapezoids AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C =  d – the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). Also covered: AF1.2, AF3.2 California Standards 1212

Holt CA Course Area of Triangles and Trapezoids

Holt CA Course Area of Triangles and Trapezoids A. Find the area of the triangle. Teacher Example 1A: Finding the Area of a Triangle 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.

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

Holt CA Course Area of Triangles and Trapezoids A. Find the area of the triangle. 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. Student Practice 1A: 6 9

Holt CA Course Area of Triangles and Trapezoids B. Find the area of the triangle. 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. Student Practice 1B: 10 7

Holt CA 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

Holt CA Course Area of Triangles and Trapezoids In the term b 1, the number 1 is called a subscript. It is read as “b-one” or “b sub-one.” Reading Math

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

Holt CA Course Area of Triangles and Trapezoids B. Find the area of the trapezoid. Teacher Example 2B: Finding the Area of a Trapezoid 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

Holt CA Course Area of Triangles and Trapezoids A. Find the area of the trapezoid. 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. Student Practice 2A: 4 in. 6 in. 11 in.

Holt CA Course Area of Triangles and Trapezoids B. Find the area of the trapezoid. 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. Student Practice 2B: 16 cm 5 cm 9 cm

Holt CA Course Area of Triangles and Trapezoids The state of Wisconsin is shaped somewhat like a trapezoid. What is the approximate area of the state? Teacher Example 3: Geometry Application 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.

Holt CA Course Area of Triangles and Trapezoids A large preserve has a similar trapezoid shape. What is the approximate area of the preserve? Student Practice 3: 232 mi 116 mi A = 1212 h(b 1 + b 2 ) Use the formula. A = 1212 · 129( ) A = 1212 · 129(348) A = 22,446 The area of the preserve is approximately 22,446 square miles. Substitute. Multiply. Add. 129 mi

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