Unit 4 Solid Geometry Math II Area of 2D Shapes

Regular Shapes All sides are congruent, all angles are congruent

2-D Shapes 3 sides  Triangle 4 sides  Quadrilateral 5 sides  Pentagon 6 sides  Hexagon 7 sides  Heptagon 8 sides  Octagon 9 sides  Nonagon 10 sides  Decagon 12 sides  Dodecagon

Area of a Square Side length s A = s Example: A = 6² = 36 sq. units

Area of a Rectangle Length l, and width w A = l × w 12 5 Example: A = 12 x 5 = 60 sq. units

Example: Find the area of a rectangle of length 12 inches and width 5 inches.

Example: You have a part-time job at a school. You need to buy enough grass seed to cover the school’s soccer field. The field is 50 yards wide and 100 yards long. The instructions on the seed bags say that one bag will cover 5000 square feet. How many bags do you need?

Area of a Triangle side lengths a, b, and c, base b, and height h Example: 7 6 A = (1/2)(7)(6) = 21 sq. units

Example: Find the area of the triangle defined by D (1, 3), E (8, 3), and F (4, 7).

Example: You are making a triangular flag with a base of 24 inches and an area of 360 square inches. How long should it be?

Area of a Circle Radius r A = πr 2 Example: 9 A = π(9) 2 = 81π = sq. units

Example: Find the area of the circle. 12 cm

Area of a Trapezoid b 1 and b 2 = “bases” of the trapezoid, are parallel Other 2 sides are the “legs” h = height of the trapezoid (from one base to the other) base 1 base 2 leg height If legs are ≅, then it is an isosceles trapezoid.

Example: Find the area of trapezoid WXYZ.

Example: Find the area of the trapezoid.

Area of a Regular Triangle Area of a Regular Triangle:

Example: Find the area of the regular Δ. 12 cm

Example: Find the area of a regular Δ with side length = 20 in.

Credits! Pictures and Problems from the following websites: teachers.henrico.k12.va.us/.../09AreaVolume/... 1Area2D/LECTURE9-1.ppt‎ McDougal Littell GEOMETRY By Larson, Boswell, and Stiff