1. 6.7 Areas of Triangles and Quadrilaterals Day #1 Geometry

2. Objectives: Find the areas of __________________________________ __________________________________

3. Using Area Formulas Postulate 22: Area of a Square Postulate –The area of a square is _____________________________________ Postulate 23: Area Congruence Postulate –If two polygons are congruent, then _____________________________________ Postulate 24: Area Addition Postulate –The area of a region is _____________________________________

4. Area Theorems Theorem 6.20 Area of a Rectangle The area of a rectangle is ________________ ________________ h b A =

5. Area Theorems Theorem 6.21 Area of a Parallelogram The area of a parallelogram is _________________ _________________ A = h b

6. Area Theorems Theorem 6.22 Area of a Triangle The area of a triangle is _________________ _________________ _________________ A = h b

7. Using the Area Theorems Find the area of  ABCD. Solution: –Method 1: –Method 2: –Notice that you get the same area with either base. 9

8. Finding the Height of a Triangle Rewrite the formula for the area of a triangle in terms of h. Then use your formula to find the height of a triangle that has an area of 12 and a base length of 6. Solution:

9. Height of a Parallelogram Find the height of a parallelogram that has an area of 96 ft 2 and a base length of 8 ft.

10. A triangle has an area of 120 and a base of 24. Are all triangles with these dimensions congruent? 10 24 10

11. Assignment pp. 376-378

12. 6.7 Areas of Triangles and Quadrilaterals Day #2 Geometry

13. Areas of Trapezoids Theorem 6.23 Area of a Trapezoid The area of a trapezoid is ___________________ ___________________ __________________ A = b1b1 b2b2 h

14. Areas of Kites Theorem 6.24 Area of a Kite The area of a kite is _________________ _________________ _________________ A = d1d1 d2d2

15. Areas of Rhombuses Theorem 6.24 Area of a Rhombus The area of a rhombus is _________________ _________________ A = d1d1 d2d2

16. Finding the Area of a Trapezoid Find the area of trapezoid WXYZ. Solution:

17. Finding the Area of a Trapezoid Substitute __ for h, __ for b 1, and __ for b 2 to find the area of the trapezoid.  The area of trapezoid WXYZ is 20 square units

18. Justification of Kite/Rhombuses Formulas The diagram at the right justifies the formulas for the areas of kites and rhombuses. The diagram show that the area of a kite is half the area of a rectangle whose length and width are the lengths of the diagonals of the kite. The same is true for a rhombus.

19. Find the area of kite ABCD 16 8 8 8 C B D A

20. Area of Rhombus Find the area of rhombus EFGH if EG = 10 and FH = 15

21. Find the Area of the Figure 4 3 4 3 3 4

22. Describe two ways to find the area of a rhombus.

23. Assignment Pg 376-378 #