This document discusses formulas for calculating the area and surface area of different shapes. It provides formulas for calculating the area of rectangles, squares, triangles, parallelograms, rhombuses, trapezoids, circles, as well as the surface area of prisms, cylinders, cones, spheres, pyramids. It also discusses converting between different units of volume. Examples are provided to demonstrate how to apply each formula.

3. 1. recognize the different formulas for area of
polygonal regions and solid figures
2. convert one unit of volume to another?

5. The inside the boundary
of a flat (2-dimensional) object such as a
triangle or circle.
The size of a surface.

6. The
inside the
boundary of a flat
(2-dimensional)
object such as a
triangle or circle.
The size of a
surface.

7. The
inside the
boundary of a flat
(2-dimensional)
object such as a
triangle or circle.
The size of a
surface.

8. The
inside the
boundary of a flat
(2-dimensional)
object such as a
triangle or circle.
The size of a
surface.
20 square
units

9. The
inside the
boundary of a flat
(2-dimensional)
object such as a
triangle or circle.
The size of a
surface.

10. The
inside the
boundary of a flat
(2-dimensional)
object such as a
triangle or circle.
The size of a
surface.

11. In area we use
to be used as its unit of
measurement.
i.e square centimeters (sq. cm)
Take note also that if is
present. We use as its unit of
measurement..

12. 𝐴 = 10 𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡
𝐴 = 10 𝑠𝑞𝑢𝑎𝑟𝑒 𝑚𝑒𝑡𝑒𝑟𝑠
𝐴 = 10 𝑠𝑞. 𝑢𝑛𝑖𝑡𝑠
𝐴 = 10 𝑠𝑞. 𝑚
𝐴 = 10 𝑚2

13. Rectangle
Square
Triangle
Parallelogram
Rhombus
Trapezoid

15. 𝐴 = 𝑙𝑤
Area of a rectangle = 𝑙𝑒𝑛𝑔𝑡ℎ × 𝑤𝑖𝑑𝑡ℎ
width (w)
Length (l)
𝐴 = 𝑠2
Area of a square = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑖𝑑𝑒 2
side (s)

16. Example 1:
3
7

17. Example 2: 36 cm
18 cm

18. Example 3:
4

19. Example 4:
12 m

20. question
s?

22. 𝐴 = 𝑏ℎ
Area of a rhombus = 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡
height (h)
base (b)
𝐴 = 𝑏ℎ
Area of parallelogram = 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡
height (h)
base (b)

23. Example 1:
8 in
3 in
8 in

24. Example 2:
28
22
28

25. Example 3:
50 cm
20 cm
50 cm

26. question
s?

28. 𝐴 =
1
2
𝑏ℎ
Area of a triangle =
1
2
× 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡
height (h)
base (b)

29. Example 1:
6 in
28 in

30. Example 1:
12 m
22 m 8 m
13 m

31. question
s?

33. 𝐴 =
1
2
ℎ( 𝑏1 + 𝑏2
)
Area of a trapezoid =
1
2
× ℎ𝑒𝑖𝑔ℎ𝑡 (𝑏𝑎𝑠𝑒1 + 𝑏𝑎𝑠𝑒2)
height (h)
base2 (𝑏2)
base1 (𝑏1)

34. Example 1:
11 ft
5 ft
4 ft

35. Example 2:
10 hm
14 hm
7 hm

36. question
s?

38. Prism
Cone
Cylinder
Sphere
Pyramid

39. Pyramid

40. Sphere

41. Cone

42. Prism

43. Cylinder

44. Prism

45. Prism
Rectangular Prism
Faces
Edge
Vertex

46. question
s?

48. The of a space figure is
the .

49. Prism
Rectangular Prism
The of a space figure is the
.

50. question
s?

52. 𝑆𝐴 = 6𝑒2
Surface Area = 6 × 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑓𝑎𝑐𝑒
e
e
e

53. Example 1:
7 cm
7 cm
7 cm

54. Example 2:
10 in
10 in
10 in

55. Example 3:
8.5 yd
8.5 yd
8.5 yd

56. question
s?

58. 𝑆𝐴 = 2𝑙𝑤 + 2ℎ𝑤 + 2ℎ𝑙
Surface Area of a Rectangular Solid
ℎ
𝑙
𝑤

59. Example 1:
ℎ = 3𝑐𝑚
𝑙 = 11 𝑐𝑚
𝑤 = 7 𝑐𝑚

60. Example 2:
ℎ = 9 𝑚
𝑙 = 4 𝑚
𝑤 = 17 𝑚

61. question
s?

63. 𝑆𝐴 = 2𝑙𝑤 + 2ℎ𝑤 + 2ℎ𝑙
Surface Area of a Rectangular Solid
ℎ
𝑙
𝑤

64. Example 1:
ℎ = 3𝑐𝑚
𝑙 = 11 𝑐𝑚
𝑤 = 7 𝑐𝑚

65. question
s?