1. 11.2 Areas of Triangles, Trapezoids, and Rhombi

2. Objectives Find areas of triangles Find areas of trapezoids Find areas of rhombi

3. Area of Triangles If the triangle has the area of A square units, a base of b units, and a height of h units, then… A=1/2bh A B C b h

4. Example 1: Find the area of the triangle if the base is 9 in. and the height is 5 in. A=1/2bh B A C 9 5

5. Example 1: Since the base is 9 in. and the height is 5 in. your equation should read, A=1/2(5x9) Solve A=1/2(45) Multiply. A=22.5 Multiply by ½. The area of triangle ABC is 22.5 square inches.

6. Area of Quadrilaterals Using Δ's The area of a quadrilateral is equal to the sum of the areas of triangle FGI and triangle GHI. A (FGHI)= ½(bh) + ½(bh) F g G I H

7. Example 2: Find the area of the quadrilateral if FH= 37 in. 18 in. 9 in. F G IH

8. Example 2: A= ½(37x9)+ ½(37x18) Solve. A= ½(333) + ½(666) Multiply. A= 166.5 + 333 Add. A= 499.5 square inches

9. Area of a Trapezoid If a trapezoid has an area of A units, bases of b1 units and b2 units and a height of h units, then… A= ½ h (b1+b2) h b2 b1

10. Example 3: Find the area of the trapezoid. 12 yd. 16 yd. 24 yd. 14 yd.

11. Example 3: A= ½x12(16+24) Add. A= ½x12(40) Multiply. A= ½(480) Multiply. A= 240 square yards.

12. Example 4: Area of a trapezoid on the coordinate plane. Since TV and ZW are horizontal, find their length by subtracting the x-coordinates from their endpoints. TV ZW (-3,4)(3,4) (-5,-1)(6,-1)

13. Example 4: TV= |-3-3| TV= |-6| TV= 6 ZW= |-5-6| ZW= |-11| ZW= 11 Because the bases are horizontal segments, the distance between them can be measured on a vertical line. That is, subtract the y-coordinates. H= |4-(-1)| H= |5| H= 5

14. Example 4: Now that you have the height and bases, you can solve for the area. A= ½h(b1+ b2) A= ½(5)(6+11) Substitution. A= ½(5)(17) Addition. A= ½(85) Multiply. A= 42.5 square units.

15. Area of Rhombi If a rhombus has an area of A square units and diagonals of d1 and d2 units, then… A= ½(d1xd2) (AC is d1, BD is d2) A B D C d1 d2

16. Example 5: Find the area of the rhombus if ML= 20m and NP= 24m. M L N P

17. Example 5: A= ½(20x24) Multiply. A= ½(480) Multiply. A= 240 Square meters.

18. Rhombus on Coordinate Plane To find the area of a rhombus on the coordinate plane, you must know the diagonals. To find the diagonals...subtract the x-coordinates to find d1, and subtract the y-coordinates to find d2.

19. Example 6: Find the area of a rhombus with the points E(-1,3), F(2,7), G(5,3), and H(2,-1) F (2,7) G (5,3) H (2,-1) E (-1,3)

20. Let EG be d1 and FH be d2 Subtract the x- coordinates of E and G to find d1 d1= |-1-5| d1= |-6| d1= 6 Subtract the y- coordinates of F and H to find d2 d2= |7-(-1)| d2= |8| d2= 8 F (2,7) G (5,3) H (2, -1) E (-1,3) d1 d2

21. Now that you have D1 and D2, solve. A= ½(d1xd2) A= ½(6x8) Multiply. A= ½(48) Multiply. A= 24 sq. units.

22. Find the Missing Measures Rhombus WXYZ has an area of 100 square meters. Find XZ if WY= 20 meters. X Y Z W

23. Use the formula for the area of a rhombus and solve for D1 (XZ) A= ½(d1xd2) 100= ½(d1)(20) Substitution. 100= 10(d1) Multiply. 10=d1 Divide. XZ= 10 meters

24. Postulate 11.1 Postulate 11.1: Congruent figures have equal areas.

25. Assignment: Pre-AP Pg. 606 #13-21, 22-28 evens, 30-35 Geometry Pg. 606 #13 – 21, 30 - 35