Geometry 11 2 Areas of Parallelograms Rhombuses and

Geometry 11. 2 Areas of Parallelograms, Rhombuses, and Triangles

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

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

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

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

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

Find the area of each figure. 7. Pythagorean Theorem/Triples 20 15 Let’s do #7! 8. This is an altitude. 7 Dropping a rock! 25 4 24 5 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 A = 5(2) A = 10 units 2

9. A triangle with base 18 and height 7. A = 9(7) 10. A triangle with sides 5, 12, 13. 12 It is a right triangle. Let’s do #10, 12! You try #13! A = 63 units 2 13 A = ½ (12)(5) A = 30 units 2 5 11. Find the area of an isosceles triangle with sides 30, and 24. h 2 + 122 = 302 Area = 12(6√ 21) 30 30 2 h + 144 = 900 h h 2 = 756 h = 6√ 21 12 Area = 72√ 21 units 2 24 12. Find the area of an isosceles triangle with base 16 and perimeter 52. h 2 + 82 = 182 Area = 8(2√ 65) 18 18 2 h + 64 = 324 h h 2 = 260 h = 2√ 65 8 Area = 16√ 65 units 2 16 13. Find the area of an equilateral triangle with sides 12 cm. 12 6√ 3 60 o 6 12 Area = 6(6√ 3) Area = 36√ 3 units 2 6√ 3 60 o 12 6 14. Find the area of an equilateral triangle with height 6√ 3. Area = 36√ 3 units 2

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

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

19. Find the area of a rhombus with diagonals 8 m and 20 m. Let’s do #20! You try #21! A = 8(10) = 80 units 2 20. Find the area of a rhombus with perimeter 52 and one diagonal 10. 13 13 12 5 A = 12(10) = 120 units 2 5 13 13 21. Find the area of a rhombus with perimeter 100 and one diagonal 14. 25 25 24 7 25 A = 14(24) = 336 units 2 7 25

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. A = short height(long base) A = short base(long height) The longer altitude is 10 units. The area is 14(5) = 70 units 2. Since A = bh 70 = 7 h 10 = h

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.