Area of Triangles and Trapezoids 8-5 Area of Triangles and Trapezoids Course 2 Warm Up Problem of the Day Lesson Presentation

Area of Triangles and Trapezoids Course 2 8-5 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 4. 3.5(12 + 8.2) 70.7

Area of Triangles and Trapezoids Course 2 8-5 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

Area of Triangles and Trapezoids Area of Triangles and Trapezoids Course 2 8-5 Area of Triangles and Trapezoids Area of Triangles and Trapezoids Learn to find the area of triangles and trapezoids.

Area of Triangles and Trapezoids Course 2 8-5 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.

Area of Triangles and Trapezoids Course 2 8-5 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

Additional Example 1A: Finding the Area of a Triangle Course 2 8-5 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.

Additional Example 1B: Finding the area of a Triangle Course 2 8-5 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.

Areas of Triangles and Trapezoids Course 2 8-5 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.

Areas of Triangles and Trapezoids Course 2 8-5 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.

Area of Triangles and Trapezoids Course 2 8-5 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).

Area of Triangles and Trapezoids Course 2 8-5 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).

Area of Triangles and Trapezoids Course 2 8-5 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

Additional Example 2A: Finding the Area of a Trapezoid Course 2 8-5 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. A = 42 Multiply. The area of the trapezoid is 42 in2.

Additional Example 2B: Finding the Area of a Trapezoid Course 2 8-5 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(12 + 16) 7 cm Substitute. 1 2 Add. A = · 7(28) 16 cm A = 98 Multiply. The area of the trapezoid is 98 cm2.

Areas of Triangles and Trapezoids Course 2 8-5 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 Add. A = · 6(15) A = 45 Multiply. The area of the trapezoid is 45 in2.

Areas of Triangles and Trapezoids Course 2 8-5 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 Add. 5 cm A = · 9(21) A = 94.5 Multiply. The area of the trapezoid is 94.5 cm2.

Area of Triangles and Trapezoids Insert Lesson Title Here Course 2 8-5 Area of Triangles and Trapezoids Insert Lesson Title Here Lesson Quiz 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