2. 6.7 Areas of Triangles and Quadrilaterals

3. Warmup 1. 2. 3.

4. Area Postulates  Area of a Square Postulate  The area of a square is the square of the length of its sides, or A = s 2.  Area Congruence Postulate  If two polygons are congruent, then they have the same area.  Area Addition Postulate  The area of a region is the sum of the areas of its non-overlapping parts.

5. Area  Rectangle: A = bh  Parallelogram: A = bh  Triangle: A = ½ bh  Trapezoid: A = ½ h(b 1 +b 2 )  Kite: A = ½ d 1 d 2  Rhombus: A = ½ d 1 d 2

6.  Find the area of ∆ ABC. A B C 7 5 64 L

7.  Find the area of a trapezoid with vertices at A(0,0), B(2,4), C(6,4), and D(9,0).

8. Find the area of the figures. 4 4 4 4 L L L L L L L L 2 5 12 8

9. Find the area of ABCD. A B C D E 12 16 9 ABCD is a parallelogram Area = bh = (16)(9) = 144

10. Find the area of a trapezoid.  Find the area of a trapezoid WXYZ with W(8,1), X(1,1), Y(2,5), and Z(5,5).

11. Find the area of rhombus.  Find the area of rhombus ABCD. A B C D 20 15 25 Area of Rhombus A = ½ d 1 d 2 = ½ (40)(30) = ½ (1200) = 600

12.  The area of the kite is160.  Find the length of BD. A B C D 10

13. Ch 6 Review Day 4 Part 2

14. Review 1  A polygon with 7 sides is called a ____. A) nonagon B) dodecagon C) heptagon D) hexagon E) decagon

15. Review 2  Find m<A A) 65° B) 135° C) 100° D) 90° E) 105° A B C D 165° 30° 65°

16. Review 3  Opposite angles of a parallelogram must be _______. A) complementary B) supplementary C) congruent D) A and C E) B and C

17. Review 4  If a quadrilateral has four equal sides, then it must be a _______. A) rectangle B) square C) rhombus D) A and B E) B and C

18. Review 5  The perimeter of a square MNOP is 72 inches, and NO = 2x + 6. What is the value of x? A) 15 B) 12 C) 6 D) 9 E) 18

19. Review 6  ABCD is a trapezoid. Find the length of midsegment EF. A) 5 B) 11 C) 16 D) 8 E) 22 A B C D E F 11 5 9 13

20. Review 7  The quadrilateral below is most specifically a __________. A) rhombus B) rectangle C) kite D) parallelogram E) trapezoid

21. Review 8  Find the base length of a triangle with an area of 52 cm 2 and a height of 13cm. A) 8 cm B) 16 cm C) 4 cm D) 2 cm E) 26 cm

22. Review 9  A right triangle has legs of 24 units and 18 units. The length of the hypotenuse is ____. A) 15 units B) 30 units C) 45 units D) 15.9 units E) 32 units

23. Review 10  Sketch a concave pentagon.  Sketch a convex pentagon.

24. Review 11  What type of quadrilateral is ABCD? Explain your reasoning. A B C D 120° 60° Isosceles Trapezoid Isosceles : AD = BC Trapezoid : AB ll CD