1. Geometry 11.2 Areas of Parallelograms, Rhombuses, and Triangles

2. Parallelogram A = bh The length of the altitude. Base Height Any side of the parallelogram The altitude is defined as any segment perpendicular to the line containing the base from any point on the opposite side.

3. Parallelogram A = bh Perpendicular to the base(altitude). Base Height Any side of the parallelogram Check this out! You would find the same area either way you solved!

4. Solve. 1.Find the area of a parallelogram with base 6 cm and corresponding height 7 cm. 2. Find the area of a parallelogram with base 6√2 and corresponding height 10√2. A = 6(7) A = 42 units 2 A = (6√2)(10√2) A = 120 units 2

5. Find the area of each parallelogram. 3. Base 12 and height 8. 4 6 12 15 10 4. 5.6. A = 12(8) A = 96 units 2 A = 12(4) A = 48 units 2 5 5√3 A = 15(5√3) A = 75√3 units 2 6 6√2 A = 6(6√2) A = 36√2 units 2 Let’s do #4,5! You try #6!

6. Triangle A = ½ bh Base Height ½ the base times the height or ½ the height times the base WHICHEVER IS EASIER! Imagine dropping a rock from the highest point down to the base to find the height. WHY IS THIS THE FORMULA?

7. Find the area of each figure. 20 25 7 4 5 7.8. Pythagorean Theorem/Triples 24 15 Total area = area of top triangle + area of bottom triangle A = ½ (15)(20) + ½ (24)(7) A = (10)(15) + (12)(7) A = 150 + 84 A = 234 units 2 This is an altitude. Dropping a rock! A = 5(2) A = 10 units 2 Let’s do #7!

8. 9. A triangle with base 18 and height 7. 10. A triangle with sides 5, 12, 13. 11. Find the area of an isosceles triangle with sides 30, 30, and 24. 12. Find the area of an isosceles triangle with base 16 and perimeter 52. 13. Find the area of an equilateral triangle with sides 12 cm. 14. Find the area of an equilateral triangle with height 6√3. A = 9(7)A = 63 units 2 It is a right triangle. 5 12 13 A = ½ (12)(5) A = 30 units 2 30 24 12 h h 2 + 12 2 = 30 2 h 2 + 144 = 900 h 2 = 756 h = 6√21 Area = 12(6√21) Area = 72√21 units 2 18 16 8 h h 2 + 8 2 = 18 2 h 2 + 64 = 324 h 2 = 260 h = 2√65 Area = 8(2√65) Area = 16√65 units 2 60 o 12 6 6√3 Area = 6(6√3) Area = 36√3 units 2 60 o 6 6√3 Area = 6(6√3) Area = 36√3 units 2 Let’s do #10,12! You try #13!

9. Rhombus A = ½ d 1 d 2 Take ½ of whichever diagonal is easier than multiply.

10. Find the area of each rhombus. 10 12 8 17 15. 16. 17. 18. A = ½ d 1 d 2 10 12 A = 10(24) A = 240 units 2 15 A = ½ d 1 d 2 A = 30(8) A = 240 units 2 4 A = ½ d 1 d 2 A = 4(8√3) A = 32√3 units 2 A rhombus is a parallelogram. 45 o 10√2 10 A = bh A = 10(10√2) A = 100√2 units 2 Let’s do #16,18! You try #17!

11. 19. Find the area of a rhombus with diagonals 8 m and 20 m. 20. Find the area of a rhombus with perimeter 52 and one diagonal 10. 21. Find the area of a rhombus with perimeter 100 and one diagonal 14. A = 8(10) = 80 units 2 13 55 12 A = 12(10) = 120 units 2 25 77 24 A = 14(24) = 336 units 2 Let’s do #20! You try #21!

12. Bonus A parallelogram has two bases and two altitudes. Its longer base is 14 and its shorter altitude is 5. If its shorter base is 7, find its longer altitude. The area is 14(5) = 70 units 2. Since A = bh 70 = 7h 10 = h The longer altitude is 10 units. A = short base(long height) A = short height(long base)

13. HW P. 431 WE (1-21 odd) P. 426-427 (20-30 Even) If you think you may get below a C-, sign up for summer school as it fills quickly…and you can always cancel.