1 / 25

Goal 11.4

Goal 11.4. Area of a Parallelogram. Define. The base of a parallelogram is the length of any one of the sides. The height of a parallelogram is the perpendicular distance between the side whose length is the base and the opposite side. Find the area of the parallelogram. =. (. ). 10.

nonnie
Télécharger la présentation

Goal 11.4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Goal 11.4 Area of a Parallelogram

  2. Define The base of a parallelogram is the length of any one of the sides. The height of a parallelogram is the perpendicular distance between the side whose length is the base and the opposite side.

  3. Find the area of the parallelogram. = ( ) 10 6 = 60 ANSWER The area of the parallelogram is 60 square centimeters. EXAMPLE 1 Finding the Area of a Parallelogram SOLUTION A =bh Write formula for area. Substitute 10 for b and 6 for h. Multiply.

  4. ANSWER ANSWER ANSWER 88 in.2 65.1 m2 39 ft2 GUIDED PRACTICE for Example 1 Find the area of the parallelogram with the given base b and height h. 1. b = 8 in., h = 11 in. 2. b = 9.3 m, h = 7 m 3. b = 3.25 ft, h = 12 ft

  5. Not drawn to scale EXAMPLE 2 Find the Base of a Parallelogram Exercising A treadmill’s belt is in the shape of a parallelogram before its ends are joined to form a loop. The belt’s area is 2052 square inches. The belt’s width, which is the height of the parallelogram, is 18 inches. Find the length of the belt, which is the base of the parallelogram.

  6. 2052 b (18) = 18 18 114 = b ANSWER The length of the treadmill’s belt is 114 inches. EXAMPLE 2 Find the Base of a Parallelogram SOLUTION A = bh Write formula for area of a parallelogram. 2052 = b (18) Substitute 2052 for A and 18 for h. Divide each side by 18. Simplify.

  7. 4. A = 56 in.2 ANSWER 7 in GUIDED PRACTICE for Example 2 Use the area A of the parallelogram to find its base b or height h.

  8. 5.A=36 mm2 ANSWER 8 mm GUIDED PRACTICE for Example 2 Use the area A of the parallelogram to find its base b or height h.

  9. 6. A =54cm2 ANSWER 6 cm GUIDED PRACTICE for Example 2 Use the area A of the parallelogram to find its base b or height h.

  10. EXAMPLE 3 Comparing Areas of Parallelograms The base of a parallelogram is 4 feet and its height is 9 feet. It is enlarged to have dimensions 3 times that of the original. Compare the areas of the parallelograms. SOLUTION The dimensions of the enlarged parallelogram are 3 times those of the original parallelogram. The larger parallelogram’s base is 3(4) = 12 feet and its height is 3(9) = 27 feet. Find the area of each parallelogram. Enlarged parallelogram Original parallelogram A = bh A = bh = 4(9) = 12(27) = 36 = 324

  11. ANSWER 324 Because the area of the enlarged = 9, 36 parallelogram is 9 times the area of original parallelogram. EXAMPLE 3 Comparing Areas of Parallelograms

  12. 7. What If? Suppose the original parallelogram in Example 3 is reduced so that the dimensions are half the original. Compare the areas. ANSWER The area of the new parallelogram is one fourth the area of the original parallelogram. GUIDED PRACTICE for Example 3

  13. Goal 11.5 Areas of Triangles and Trapezoids

  14. Base/Height of Triangle • The base of a triangle is the length of any one of the sides. • The height of a triangle is the perpendicular distance between the side whose length is the base and the vertex opposite that side.

  15. Museums The Rock and Roll Hall of Fame and Museum in Cleveland, Ohio, has a triangular shaped wall as shown. What is the area of the wall? 1 A = bh 2 1 (231) (111) = 2 12,820.5 = ANSWER The area of the wall is 12,820.5 square feet. EXAMPLE 1 Finding the Area of the Triangle SOLUTION Write formula for area of a triangle. Substitute 231 for b and 111 for h. Multiply.

  16. ANSWER ANSWER ANSWER 45.5 m2 44.8 in.2 19.35 ft2 GUIDED PRACTICE for Example 1 Find the area of the triangle with the given base band heighth. 1. b = 7 m, h = 13 m 2. b = 6.4 in., h = 14 in. 3. b = 4.5 ft, h = 8.6 ft.

  17. Write formula for area of a triangle. 1 bh A = 2 1 (87) b 7525.5 = 2 43.5b 7525.5 = ANSWER The base of the triangle is about 173 feet. EXAMPLE 2 Find the Base of the Triangle Flatiron Building: From above, the Flatiron Building in New York has a shape that can be approximated by a right triangle with a height of 87 feet. The area of the triangle is 7525.5 square feet. Find its base. Substitute 7525.5 for A and 87 for h. Simplify 173 = b Divide each side by 43.5.

  18. 4. A = 61.6 m2, b = 11 m, h = ? 5. A = 108.5 ft2, b = ? , h = 14 ft ANSWER ANSWER 11.2 m 15.5 ft for Example 2 GUIDED PRACTICE Find the unknown base bor heighth of the triangle.

  19. Bases/Height of Trapezoid • The lengths of the parallel sides of a trapezoid are the bases of a trapezoid. • The height of a trapezoid is the perpendicular distance between the bases.

  20. Find the area of the trapezoid shown. 1 A = (b1 + b2) h 2 1 (5 + 10)(8) = 2 ANSWER The area of the trapezoid is 60 square feet. EXAMPLE 3 Finding the Area of a Trapezoid Write formula for area of a trapezoid. Substitute 5 for b1,10 for b2, and 8 forh. = 60 Simplify.

  21. 1 1 1 A= (b1 + b2)h 2 2 2 66= (8 + 14)h 66= (22)h 66= 11h ANSWER The height of the trapezoid is 6 meters. EXAMPLE 4 Finding the Height of a Trapezoid A trapezoid has an area of 66 square meters. The bases are 8 meters and 14 meters. Find the height. Write formula for area of a trapezoid. Substitute 66 for A, 8 for b1,14 for b2 Add Multiply 6 = h Divide each side by 11

  22. EXAMPLE 5 Standardized Test Practice

  23. 1 A = (6 + 8)(5) 2 ANSWER The area of the garden is 47 square yards.The correct answer is C. STEP 2 STEP 1 Find the area of the triangle and the trapezoid. 1 A = (8)(3) 2 EXAMPLE 5 Standardized Test Practice SOLUTION Area of the triangle = 12 Area of the trapezoid = 35 Add the areas to find the total area: 12 + 35 = 47

  24. ANSWER ANSWER 84 in.2 18 m 7. A = 216 m2 , b1 = 11 m, b2 = 13 m, h = ? GUIDED PRACTICE for Examples 3, 4 and 5 Find the unknown area Aor heighth of the trapezoid. 6. A = ? , b1 = 13 in., b2 = 15 in., h = 6 in.

  25. 8. Find the area of the figure. ANSWER 68.5 in.2 GUIDED PRACTICE for Examples 3, 4 and 5

More Related