Civil Service Exam (Subprofessional) Numerical Ability — Geometry — Perimeter, Area, Circumference & VolumeCheat Sheet
Geometry — Perimeter, Area, Circumference & Volume cheat sheet — the reference card you wish you had on exam day. Condensed from the full study notes, this is the high-yield core of Geometry — Perimeter, Area, Circumference & Volume for Civil Service Exam (Subprofessional) Numerical Ability. Download, print, revise.
Exam context
The Career Service Examination — Subprofessional Level is conducted by Civil Service Commission (CSC) and is scheduled for Bi-annual — March and August 2026. The Numerical Ability subtest is marked as "~25% weightage" in the official pattern, and Geometry — Perimeter, Area, Circumference & Volume appears in position 8th of 9 in the Civil Service Exam (Subprofessional) Numerical Ability review rotation. Passing mark: 80%. Recent Civil Service Exam (Subprofessional) 2026 papers have drawn roughly 17 questions from this subject.
Geometry — Perimeter, Area, Circumference & Volume - Cheat sheet
Your last-minute revision companion for mastering geometry calculations on Philippine entrance exams
Sections
Formulas
Formula
P = 4s
Meaning
P = perimeter, s = side length
Watch Out
Don't confuse with area formula s²
When To Use
Finding perimeter of any square
Formula
P = 2L + 2W or P = 2(L + W)
Meaning
P = perimeter, L = length, W = width
Watch Out
Make sure to multiply BOTH length and width by 2
When To Use
Finding perimeter of any rectangle
Formula
P = a + b + c
Meaning
P = perimeter, a, b, c = side lengths
Watch Out
Must add ALL three sides, not just two
When To Use
Finding perimeter of any triangle
Formula
P = 2(b + h)
Meaning
P = perimeter, b = base, h = height (slant side)
Watch Out
h here is the slant height, not perpendicular height
When To Use
Finding perimeter of parallelogram
Formula
P = a + b + c + d
Meaning
P = perimeter, a, b, c, d = all four sides
Watch Out
Add all four individual sides, not just bases
When To Use
Finding perimeter of trapezoid
Section Title
Perimeter Formulas
Important Facts
- Perimeter is always measured in linear units (cm, m, ft)
- For regular polygons: P = n × s (n = number of sides, s = side length)
- Equilateral triangle: all three sides are equal
- Perimeter problems often give total and ask for individual side
Key Definitions
Term
Perimeter
Example
Fence around a rectangular lot
Definition
Total distance around the boundary of a closed shape
Term
Regular Polygon
Example
Square, equilateral triangle, regular hexagon
Definition
Polygon with all sides equal and all angles equal
Diagrams To Know
- Square with labeled sides
- Rectangle with length and width marked
- Triangle with three sides labeled
Formulas
Formula
A = s²
Meaning
A = area, s = side length
Watch Out
Remember to square the side, not multiply by 4
When To Use
Finding area of any square
Formula
A = L × W
Meaning
A = area, L = length, W = width
Watch Out
Length times width, not length plus width
When To Use
Finding area of any rectangle
Formula
A = (1/2) × b × h
Meaning
A = area, b = base, h = perpendicular height
Watch Out
Must use perpendicular height, not slant side
When To Use
Finding area of any triangle
Formula
A = b × h
Meaning
A = area, b = base, h = perpendicular height
Watch Out
Use perpendicular height, not the slant side length
When To Use
Finding area of parallelogram
Formula
A = (1/2) × (a + b) × h
Meaning
A = area, a and b = parallel sides, h = height
Watch Out
Add the two parallel bases first, then multiply by height and divide by 2
When To Use
Finding area of trapezoid
Section Title
Area Formulas
Important Facts
- Area is always measured in square units (cm², m², ft²)
- Triangle area formula works for ALL triangles (right, acute, obtuse)
- For parallelograms, height must be perpendicular to base
- Trapezoid has exactly one pair of parallel sides
Key Definitions
Term
Area
Example
Floor space of a room
Definition
Amount of space inside a closed shape
Term
Base
Example
Bottom side of triangle
Definition
Bottom side of a shape, or any side chosen as reference
Term
Height
Example
Vertical distance in triangle
Definition
Perpendicular distance from base to opposite side
Diagrams To Know
- Rectangle with dimensions labeled
- Triangle showing base and height
- Trapezoid with parallel sides and height marked
Formulas
Formula
C = 2πr
Meaning
C = circumference, π = 3.14, r = radius
Watch Out
Don't forget to multiply by 2 when using radius
When To Use
Finding distance around a circle
Formula
C = πd
Meaning
C = circumference, π = 3.14, d = diameter
Watch Out
When given diameter, don't multiply by 2
When To Use
Finding circumference when diameter is given
Formula
A = πr²
Meaning
A = area, π = 3.14, r = radius
Watch Out
Must square the radius, not multiply by 2
When To Use
Finding area inside a circle
Formula
d = 2r
Meaning
d = diameter, r = radius
Watch Out
Diameter is always twice the radius
When To Use
Converting between diameter and radius
Common Values
Value
3.14 or 22/7
Symbol
π
Quantity
Pi
Section Title
Circle Formulas
Important Facts
- π (pi) ≈ 3.14 or 22/7 in most problems
- Radius is half the diameter: r = d/2
- Diameter is twice the radius: d = 2r
- Circumference is the perimeter of a circle
Key Definitions
Term
Circumference
Example
Length of wire needed to make a circular ring
Definition
Distance around the outside of a circle
Term
Radius
Example
Half the width of a circular table
Definition
Distance from center to any point on the circle
Term
Diameter
Example
Width of a circular pizza
Definition
Distance across circle through the center
Diagrams To Know
- Circle with radius drawn from center
- Circle with diameter drawn across
- Circle showing both radius and diameter
Formulas
Formula
V = s³
Meaning
V = volume, s = side length
Watch Out
Cube the side length (s × s × s), not square it
When To Use
Finding volume of a cube
Formula
V = L × W × H
Meaning
V = volume, L = length, W = width, H = height
Watch Out
Must multiply all three dimensions together
When To Use
Finding volume of rectangular prism
Formula
V = πr²h
Meaning
V = volume, π = 3.14, r = radius, h = height
Watch Out
Square the radius first, then multiply by π and height
When To Use
Finding volume of cylinder
Formula
V = (4/3)πr³
Meaning
V = volume, π = 3.14, r = radius
Watch Out
Must cube the radius and multiply by 4/3
When To Use
Finding volume of sphere
Formula
V = (1/3) × B × h
Meaning
V = volume, B = base area, h = height
Watch Out
Don't forget to divide by 3
When To Use
Finding volume of pyramid or cone
Common Values
Value
3.14
Symbol
π
Quantity
Pi
Section Title
Volume Formulas
Important Facts
- Volume is always measured in cubic units (cm³, m³, ft³)
- Prism volume = Base area × Height
- Pyramid/cone volume = (1/3) × Base area × Height
- Sphere is perfectly round in all directions
Key Definitions
Term
Volume
Example
Water capacity of a tank
Definition
Amount of space occupied by a three-dimensional object
Term
Cube
Example
Dice, Rubik's cube
Definition
3D shape with all edges equal and all faces square
Term
Cylinder
Example
Tin can, water tank
Definition
3D shape with circular base and top, straight sides
Diagrams To Know
- Cube with side length labeled
- Cylinder with radius and height marked
- Rectangular prism with L, W, H labeled
Must Remember
- Perimeter = add all sides; Area = multiply dimensions
- Circle: C = 2πr, A = πr²; π ≈ 3.14
- Triangle area = (1/2) × base × height (ALWAYS divide by 2)
- Volume always uses cubic units (cm³, m³)
- Cube volume = s³ (side cubed)
- Cylinder volume = πr²h (circle area × height)
- Radius = diameter ÷ 2; Diameter = radius × 2
- Rectangle area = length × width (NOT length + width)
- Trapezoid area = (1/2)(b₁ + b₂)h
- Always check units in your final answer
Last Minute Tips
- Draw a quick sketch of the shape and label given measurements
- If given perimeter, work backwards to find individual sides
- For word problems, identify the shape first, then choose the right formula
- Double-check whether you need perimeter (around) or area (inside)
- When calculating with π, leave answer as πr² or use 3.14 as specified
Comparison Tables
Rows
Values
- Distance around
- Space inside
- Space occupied
Property
Measures
Values
- Linear (cm, m)
- Square (cm², m²)
- Cubic (cm³, m³)
Property
Units
Values
- 1D boundary
- 2D surface
- 3D object
Property
Dimension
Columns
- Property
- Perimeter
- Area
- Volume
Table Title
Perimeter vs Area vs Volume
Rows
Values
- P = 4s
- A = s²
- All sides equal
Property
Square
Values
- P = 2L + 2W
- A = L × W
- Opposite sides equal
Property
Rectangle
Values
- P = a + b + c
- A = (1/2)bh
- Three-sided polygon
Property
Triangle
Columns
- Shape
- Perimeter
- Area
- Special Property
Table Title
Square vs Rectangle vs Triangle
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