Area and Volume Notes, Study notes of Mathematics

These are preliminary notes to the Area and Volume topic in Maths.

Typology: Study notes

2022/2023

Uploaded on 04/24/2023

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P e r i m e t e r :
Perimeter is the distance around a closed shape; it is the sum of the length of the
sides of the shape.
All units must be the same length when calculating perimeter
Sides with the same type of markings (dashes) are at equal length
Ex.
y
z
V o l u m e :
Area of cross section x perpendicular height
Ah
Area of a circle (
𝜋𝑟
) x perpendicular height
V = pie *radius ^2 *height
h
M e t r i c u n i t s a n d c o n v e r s i o n s :
Metric units for perimeter:
×1000 ×100 ×10
km m cm mm
÷1000 ÷100 ÷10
Metric units for area (measured in units^2):
X
P = 2x + 2y + 2z
a
Metric units for volume (measured in units^3):
Chapter 5: Area and Volume .
Tuesday, 12 October 2021
5:29 PM
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P e r i m e t e r : Perimeter is the distance around a closed shape; it is the sum of the length of the sides of the shape. ○ All units must be the same length when calculating perimeter ○ Sides with the same type of markings (dashes) are at equal length

Ex. y z V o l u m e :

  • Volume of a solid is the amount of space it occupies Volume of a prism = ◊ Area of cross section x perpendicular height ◊ Ah

Volume of a cylinder = (circular prism) ○ Area of a circle (𝜋𝑟ଶℎ) x perpendicular height ○ V = pie * radius ^ 2 * height

h M e t r i c u n i t s a n d c o n v e r s i o n s :

  • Metric units for perimeter: × 1000 × 100 × 10 km m cm mm ÷ 1000 ÷ 100 ÷ 10
  • Metric units for area (measured in units^2): X ∴ P = 2x + 2y + 2z a
  • Metric units for volume (measured in units^3):

Chapter 5: Area and Volume.

Tuesday, 12 October 2021 5:29 PM

C i r c l e s : Parts of a circle: ○ Diameter ○ Arc ○ Sector ○ Quadrant ○ Semicircle ○ Chord ○ Segment ○ Tangent ○ Radius

Notes: ○ Circles have infinite symmetry ○ Pie = 22/

  • Circumference (perimeter of a circle): C = pie * diameter OR. C = 2 * pie * radius (1/2 of diameter) = 𝜋𝑑 (^) = 2𝜋𝑟 The area of a circle: ○ A = pie * radius = A = πr^ 2 [1.e. ௔ ○ ௥మ = 𝜋]
  • The area of a semicircle, and a quadrant: A r e a :
  • Area is the amount of space taken by the shape
  • The area of a composite shape can be found by adding or subtracting the area of other basic shapes
  • Area formulas: ○ Square ○ Parallelogram ○ Rectangle ○Triangle ○ Trapezium ○Rhombus

P =

ଶగ௥ ଶ +^ 𝑑