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Perimeter Area and Circumference

Perimeter Area and Circumference. The perimeter of a polygon is the distance around the outside of the polygon. It’s equal to the sum of the lengths of the sides of the polygon. The area of a figure can be thought of as the space in the plane that the figure takes up.

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Perimeter Area and Circumference

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  1. Perimeter Area and Circumference The perimeter of a polygon is the distance around the outside of the polygon. It’s equal to the sum of the lengths of the sides of the polygon. The area of a figure can be thought of as the space in the plane that the figure takes up. The distance around the outside of a circle is called the circumference, rather than the perimeter

  2. Unit Square A unit square is a square whose sides are each one unit in length. The unit can be inches, meters, miles, centimeters or any other length measurement. We say the area of the unit square equals one square unit (1 sq. in., or 1 sq. m. etc.) Area = 1 sq. unit

  3. Rectangle A rectangle is a quadrilateral with 4 right angles.

  4. Rectangle l w w l To find the perimeter of a rectangle we need to know the length of its sides, l and w. Because opposite sides are equal we get the formula Perimeter = 2l + 2w

  5. Rectangle width length To find the area of a rectangle see how many unit squares will fit in it. The number of unit squares that will fit in the rectangle equals the area of the rectangle. Notice that the total number of unit squares that will fit in the rectangle equals the number of squares across times the number of squares down. This leads us to Area = length x width

  6. Rectangle w = 6 ft. l = 23 ft. What is the perimeter of this rectangle?

  7. Rectangle w = 6 ft. l = 23 ft. Perimeter = 2l + 2w = 2(23) + 2(6) = 46 + 12 = 58 ft.

  8. Rectangle w = 6 ft. l = 23 ft. What is the area of this rectangle?

  9. Rectangle w = 6 ft. l = 23 ft. Area = 23 x 6 = 138 sq. ft.

  10. Square A square is a special type of rectangle with length = width. If we call the length of a side s then Perimeter = 4s Area = s2

  11. Square 5.5 yds What is the perimeter of this square?

  12. Square 5.5 yds Perimeter = 4s = 4(5.5) = 22.0 yds.

  13. Square 5.5 yds What is the area of this square?

  14. Square 5.5 yds Area = = = 30.25 sq. yds.

  15. PARALLELOGRAM A parallelogram is a quadrilateral with opposite sides parallel. Opposite sides are also equal.

  16. PARALLELOGRAM s b The perimeter of a parallelogram is equal to the sum of the lengths of its sides. Because opposite sides are equal we get Perimeter = 2b + 2s

  17. PARALLELOGRAM To find the area of a parallelogram drop a line from the upper corner to the line below, forming a right triangle.

  18. PARALLELOGRAM Move the created triangle to the other side of the parallelogram...

  19. ...creating a rectangle whose area is the same as the original parallelogram. The area of the rectangle is equal to the base of the parallelogram times its height. Thus the area of the parallelogram itself is equal to its base times its height height base Area = (base) x (height)

  20. PARALLELOGRAM height base Area = (base)(height)

  21. PARALLELOGRAM 150 in. 175 in. 230 in. What is the perimeter of this parallelogram?

  22. PARALLELOGRAM 150 in. 175 in. 230 in. Perimeter = 2b + 2s = 2(230) + 2(175) = 460 + 350 = 810 in.

  23. PARALLELOGRAM 150 in. 175 in. 230 in. What is the area of this parallelogram?

  24. PARALLELOGRAM 150 in. 175 in. 230 in. Area = 230 x 150 = 34,500 sq. in.

  25. PARALLELOGRAM 10.5 yds. 12.5 yds. 7 yds. What is the perimeter of this parallelogram?

  26. PARALLELOGRAM 10.5 yds. 12.5 yds. 7 yds. Perimeter = 2b + 2s = 2(7) + 2(12.5) = 14 + 25 = 39 yds.

  27. PARALLELOGRAM 12.5 yds. 10.5 yds 7 yds. What is the area of this parallelogram?

  28. PARALLELOGRAM 12.5 yds. 10.5 yds 7 yds. Area = 7 x 10.5 = 73.5 sq. yds.

  29. TRIANGLE A triangle is a three sided figure.

  30. TRIANGLE s1 s2 s3 The perimeter of a triangle equals the sum of the lengths of its sides. Perimeter =s1 + s2 + s3

  31. TRIANGLE To determine the area of a triangle begin by drawing a second triangle the exact size and shape of the first but rotated 180 degrees (upside down)...

  32. TRIANGLE …line the two triangles up to make a parallelogram which will be twice the area of either triangle. For a parallelogram we already know Area = (base) x (height). From this we can conclude that for a triangle its area will be 1/2(base)(height) height base

  33. TRIANGLE height base Area = 1/2 (base)(height)

  34. TRIANGLE 9.5 ft. 7 ft. 5 ft 11.5 ft. What is the perimeter of this triangle?

  35. TRIANGLE 9.5 ft. 7 ft. 5 ft 11.5 ft. Perimeter = s1 + s2 + s3 = 11.5 + 7 + 9.5 = 28.0 ft.

  36. TRIANGLE 9.5 ft. 7 ft. 5 ft 11.5 ft. What is the area of this triangle?

  37. TRIANGLE 5 ft 11.5 ft. Area = (1/2)(base)(height)= (1/2)(11.5)(5) = 28.75 sq. ft.

  38. TRIANGLE 43 cm. 45 cm. 58 cm. 39 cm. What is the perimeter of this triangle?

  39. TRIANGLE 43 cm. 45 cm. 58 cm. 39 cm. Perimeter = s1 + s2 + s3 = 39 + 45 + 58 = 142 cm.

  40. TRIANGLE 43 cm. 45 cm. 58 cm. 39 cm. What is the area of this triangle?

  41. TRIANGLE 43 cm. 45 cm. 58 cm. 39 cm. Area = (1/2)(base)(height) = (1/2)(39)(43) = 838.5 sq. cm.

  42. TRAPEZOID b B A trapezoid is a quadrilateral with 2 sides parallel. The two parallel sides are called the bases and are labeled B and b.

  43. TRAPEZOID b h h B To find the area start by drawing a diagonal line making two triangles. The area of the lower triangle is (1/2)(B)(h). The area of the upper triangle is (1/2)(b)(h). The height of both triangles is h, the distance between the two bases.

  44. TRAPEZOID b h h B The area of the trapezoid is the sum of the areas of the two triangles. Area = (1/2)(B)(h) + (1/2)(b)(h) Factoring (1/2)(h) out of each term we get Area = (1/2)(h)(B + b)

  45. Trapezoid 20 in. 21 in. 21 in. 18 in. 50 in. What is the perimeter of this trapezoid?

  46. Trapezoid 20 in. 21 in. 21 in. 18 in. 50 in. Perimeter = B + b + s1 + s2 = 50 + 20 + 21 + 21 = 112 in.

  47. Trapezoid 20 in. 18 in. 50 in. Area = (1/2)(h)(B + b) = (1/2)(18)(50 + 20) = 630 sq. in.

  48. Trapezoid 33 m. 9 m. 16 m. What is the area of this trapezoid?

  49. Trapezoid 33 m. 9 m. 16 m. Area = (1/2)(h)(B + b) = (1/2)(9)(33 + 16) =220.5 sq. m.

  50. Circle A circle is the set of points which are all the same distance from a given point called the center. The diameter (d) is the length of a segment drawn from one side of the circle to the other going through the center. The radius (r) is the length of a segment drawn from the center to a point on the circle. The radius equals 1/2 the diameter. The circumference (C) is the distance around the outside of the circle. For any circle, regardless of its size, the ratio C/d is the constant  (approx. 3.14159). This leads us to the formula Circumference = d = 2r r d The area of a circle is Area = r2

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