N S O S E L Areas of Triangles and Trapezoids Goal: Find the areas of triangles and trapezoids. Vocabulary Base of The base of a triangle is the length of any one of a triangle: its sides. The height of a triangle is the perpendicular distance Height of between the side whose length is the base and the a triangle: vertex opposite that side. Bases of a The lengths of the parallel sides of a trapezoid are trapezoid: the bases of a trapezoid. Height of The height of a trapezoid is the perpendicular a trapezoid: distance between the bases. Area of a Triangle Words The area A of a triangle is half the product of a base and the corresponding height . height h Algebra ϭ ᎏ1ᎏ base b A 2bh EXAMPLE 1 Finding the Area of a Triangle Sculpture An artist is creating a sculpture that includes a triangular face that has a base 125 feet long and a height of 84 feet. Find the area of the triangular face. 84 ft Solution Write formula for area A ϭ ᎏ1ᎏbh 2 of a triangle. 125 ft ϭ ᎏ1ᎏ 125 84 2 ΂΃΂΃Substitute 125 for b and 84 for h. ϭ 5250 Multiply. Answer: The area of the face is 5250 square feet . Lesson 11.5 Areas of Triangles and Trapezoids | 251 EXAMPLE 2 Finding the Base of a Triangle A triangle has a height of 15 centimeters and an area of 202.5 square centimeters. Find the base of the triangle. 1 A ϭ ᎏᎏbh Write formula for area of a triangle. 2 1 202.5 ϭ ᎏᎏb(15) Substitute 202.5 for A and 15 for h. 2 202.5 ϭ 7.5b Simplify. 27 ϭ b Divide each side by 7.5 . Answer: The base of the triangle is 27 centimeters . Guided Practice Find the unknown area or height of the triangle. 1. A ___,? b ϭ 7 ft, h ϭ 12 ft 2. A ϭ 52 m2, b ϭ 8 m, h ___? 42 ft2 13 m Because a trapezoid has more Area of a Trapezoid than one base, the Words The area A of a trapezoid is base b bases of a trapezoid are half 1 b usually labeled 1 the product of the sum of the bases and b b and 2. 1 is read height h "b sub one." theheight . base b2 1 Algebra A ϭ ᎏᎏ(b ϩ b )h 2 1 2 252 | Chapter 11 Notetaking Guide EXAMPLE 3 Finding the Area of a Trapezoid Find the area of the trapezoid shown. 8 in. ϭ ᎏ1ᎏ ϩ A 2(b1 b2)h Write formula for area of a trapezoid. 7 in. ϭ ᎏ1ᎏ ϩ 2 ΂ 8 3 ΃΂7 ΃ Substitute 8 for b1, 3 3 in. for b2, and 7 for h. ϭ 38.5 Simplify. Answer: The area of the trapezoid is 38.5 square inches . EXAMPLE 4 Finding the Height of a Trapezoid A trapezoid has an area of 82 square meters. The bases are 11 meters and 9 meters. Find the height. ϭ ᎏ1ᎏ ϩ A 2(b1 b2)h Write formula for area of a trapezoid. Substitute 82 for A,11 for b1, ϭ ᎏ1ᎏ ϩ 82 2 ΂ 11 9 ΃h and9 for b2. ϭ ᎏ1ᎏ 82 2 ΂΃20 h Add. 82 ϭ 10 h Multiply. 8.2 ϭ h Divide each side by 10 . Answer: The height of the trapezoid is 8.2 meters . Guided Practice Find the unknown area, base, or height of the trapezoid. ϭ ϭ ϭ 3. A ___,? b1 12 ft, b2 8 ft, h 4 ft 40 ft2 2 ϭ ϭ ϭ 4. A 22 m , b1 7 m, b2 ___,? h 4 m 4 m 2 ϭ ϭ ϭ 5. A 15 cm , b1 3 cm, b2 7 cm, h ___? 3 cm Lesson 11.5 Areas of Triangles and Trapezoids | 253.