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 1 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 1 bh 2 of a triangle. 125 ft
1 125 84 2 Substitute 125 for b and 84 for h.
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 bh Write formula for area of a triangle. 2 1 202.5 b(15) Substitute 202.5 for A and 15 for h. 2
202.5 7.5b Simplify.
27 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 7 ft, h 12 ft 2. A 52 m2, b 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 (b 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.
1 A 2(b1 b2)h Write formula for area of a trapezoid. 7 in. 1 2 8 3 7 Substitute 8 for b1, 3
3 in. for b2, and 7 for h. 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.
1 A 2(b1 b2)h Write formula for area of a trapezoid.
Substitute 82 for A,11 for b1, 1 82 2 11 9 h and9 for b2.
1 82 2 20 h Add.
82 10 h Multiply.
8.2 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.
3. A ___,? b1 12 ft, b2 8 ft, h 4 ft
40 ft2 2 4. A 22 m , b1 7 m, b2 ___,? h 4 m
4 m 2 5. A 15 cm , b1 3 cm, b2 7 cm, h ___?
3 cm
Lesson 11.5 Areas of Triangles and Trapezoids | 253