1. Sect. 6.7 Areas of Triangles and Quadrilaterals Goal 1 Using Area Formulas Goal 2 Areas of Trapezoids, Kites and Rhombuses

2. What Is Area ? Area is the amount of space inside a shape: Area Area is measured in square units 1cm A square centimeter is a square measuring one centimeter in each direction. It can be written as : 1cm 2 Using Area Formulas

3. Area Postulates Postulate 22: Area of a Square Postulate The area of a square is the square of the length of a side A = s 2 Postulate 23: Area Congruence Postulate If two polygons are congruent, then they have the same area. Postulate 24: Area Addition Postulate The area of a region is the sum of the areas of its nonoverlapping parts.

4. Using Area Formulas Area = Base · Height A = bh Area of a Rectangle

5. Using Area Formulas Find the area of the shapes below : (1) 8cm 6cm 4.2m 2.7m (2) (3) 17cm 8cm 12cm 5cm Example 1

6. Using Area Formulas 7cm 10cm 8cm 3cm 7cm 2cm 8cm 3cm X Y Example 2

7. Using Area Formulas Area of a Parallelogram Area = Base · Height A = bh

8. Using Area Formulas Find the area of a parallelogram with a base of 12 centimeters and a height of 5 centimeters. Example 3

9. Using Area Formulas Find the Area of the Parallelogram Example 4

10. The Area Of A Triangle. Consider the right angled triangle below: Of what shape is the triangle half? Rectangle 8 cm 5cm What is the area of the rectangle? Area = 8 x 5 = 40 cm 2 What is the area of the triangle ? Area = ½ x 40 = 20cm 2 Base Height Formula for Area of a Triangle is: Area = ½ x Base x Height A = ½ BH

11. Using Area Formulas Calculate the area of the triangle below: 10cm 6cm Example 5

12. Using Area Formulas 6.4m 3.2m Calculate the area of the triangle below: Example 6

13. Using Area Formulas Example 7 Calculate the area of the triangle below:

14. Areas of Trapezoids, Kites and Rhombuses Area of a Trapezoid Area = ½ h ( b 1 + b 2 ) (b 1 ) (b 2 )

15. Calculate the area of the trapezoid below : 16cm 11cm 13cm Example 8 Areas of Trapezoids, Kites and Rhombuses

16. Example 9 Find the Area of Trapezoid EFGH Area = ½ h ( b 1 + b 2 )

17. Areas of Trapezoids, Kites and Rhombuses Area of a Kite Area of a Kite is one-half the product of the lengths of the diagonals

18. Areas of Trapezoids, Kites and Rhombuses Example 10 Find the Area of Kite ABCD

19. Areas of Trapezoids, Kites and Rhombuses Area of a Rhombus Area of a Rhombus is one-half the product of the lengths of the diagonals

20. Areas of Trapezoids, Kites and Rhombuses Example 11 Find the Area of rhombus EFGH is EG = 15 and FH = 10

21. Homework: pp. 376 Exs. 14-34 all