1. Perimeter The perimeter of a polygon is the sum of the lengths of the sides Example 1: Find the perimeter of  ABC O A(-1,-2) B(5,-2) C(5,6) AB = 5 – (-1) = 6 BC = 6 – (-2) = 8 AC = = AB + BC + AC = 6 + 8 + 10 = 24

2. Area of Squares and Rectangles The area of a square is the length of the sides squared. A = s 2 The area of a rectangle is the product of its base and height. A = bh b h s s

3. Area of Parallelograms The area of a parallelogram is the product of any base and its corresponding height. A = bh Any side can be a base h b An altitude is a segment  to the base drawn to the opposite base The height is the length of the altitude

4. Example 2 In parallelogram ABCD, DE and CF are altitudes. Find CF. AEB 10 F C D 12 13 A = bh = 10(12) = 120 A = bh = 13(CF) = 120 CF = 120/13  9.2 units 2

5. Area of Triangles The area of a triangle is half the product of any base and the corresponding height h b A =

6. Example 3 Find the area of the Triangle 8 7 A = ½ bh A = (½) (7) (8) = 28 units 2 Try it when b = 15 and h = 12 A = ½ bh = (½) (15) (12) = 90 units 2

7. Area of 45-45-90 Triangles The area of a 45-45-90 right triangle is one half of its leg length squared. A = ½ s 2 s s s2s2 45°

8. Example 4 A = Find the area of the 45-45-90 right triangle. 5  6 cm 45° = 37.5 cm 2

9. Area of 30-60-90 Triangles The area of a 30-60-90 right triangle is: 2s s s3s3 30° 60° A =

10. Example 5 Find the area of the 30-60-90 right triangle. Leave your answer in simple radical form. 4 in 30° 60° A = = in 2

11. Area of Trapezoids b2b2 b1b1 h The area of a Trapezoid is half the product of the height and the sum of the two bases. A =

12. Example 6 h = 5m Find the area of trapezoid DUCK. 5m h 60° D U CK 2m A = = =