FEUCAT Mathematics — Perimeter, Area, Volume & Equation of a LineCheat Sheet
Cheat sheet for FEUCAT Mathematics — Perimeter, Area, Volume & Equation of a Line. Compact, printable, and organised around the concepts Far Eastern University tests most frequently in the FEUCAT 2026. Perfect for the week before exam day.
Exam context
For the Far Eastern University College Admission Test, Far Eastern University tests Mathematics under a "Core section" label, with Perimeter, Area, Volume & Equation of a Line in the 6th slot across 9 chapters. FEUCAT candidates must clear the Competitive overall score cut on the 2026 paper, which draws about a meaningful share of Mathematics questions. Date to watch: Q3–Q4 2026.
Perimeter, Area, Volume & Equation of a Line - Cheat sheet
Your last-minute revision companion for mensuration formulas and line equations — the most tested geometry topics in UPCAT
Sections
Formulas
Formula
P = 2(l + w)
Meaning
P = perimeter, l = length, w = width
Watch Out
Don't square the values — perimeter is just the sum of sides
When To Use
For rectangles when both length and width are given
Formula
P = 4s
Meaning
P = perimeter, s = side length
Watch Out
Remember it's 4 times ONE side, not the area formula
When To Use
For squares when one side is given
Formula
P = a + b + c
Meaning
P = perimeter, a, b, c = the three sides
Watch Out
Make sure all three sides are in the same units
When To Use
For any triangle when all three sides are known
Formula
C = 2πr = πd
Meaning
C = circumference, r = radius, d = diameter
Watch Out
If given diameter, don't forget to divide by 2 for radius formulas
When To Use
For circles — use 2πr when radius is given, πd when diameter is given
Formula
P = ns
Meaning
P = perimeter, n = number of sides, s = side length
Watch Out
Only works for REGULAR polygons where all sides are equal
When To Use
For regular polygons (all sides equal)
Common Values
Value
3.14159...
Symbol
π
Quantity
Pi (π)
Value
22/7
Symbol
π
Quantity
Pi approximation
Section Title
Perimeter Formulas
Important Facts
- Perimeter units are always linear (cm, m, ft) — never squared
- For composite shapes, add the outer edges only
- π ≈ 3.14159 or use 22/7 for quick calculations
Key Definitions
Term
Perimeter
Example
Walking around the edge of a basketball court
Definition
The total distance around the outside of a 2D shape
Term
Circumference
Example
The distance around a wheel's rim
Definition
The perimeter of a circle
Diagrams To Know
- Rectangle with labeled length and width
- Circle with labeled radius and diameter
Formulas
Formula
A = lw
Meaning
A = area, l = length, w = width
Watch Out
Make sure length and width are perpendicular to each other
When To Use
For rectangles and when you have perpendicular sides
Formula
A = s²
Meaning
A = area, s = side length
Watch Out
Don't confuse with perimeter — this one is SQUARED
When To Use
For squares when one side is given
Formula
A = ½bh
Meaning
A = area, b = base, h = height (perpendicular to base)
Watch Out
Height must be perpendicular to the base, not just any side
When To Use
For triangles when base and height are known
Formula
A = πr²
Meaning
A = area, r = radius
Watch Out
Don't forget to SQUARE the radius — most common mistake
When To Use
For circles when radius is given
Formula
A = bh
Meaning
A = area, b = base, h = height
Watch Out
Use height, not the slanted side length
When To Use
For parallelograms when base and height are known
Formula
A = ½(b₁ + b₂)h
Meaning
A = area, b₁ and b₂ = parallel sides, h = height
Watch Out
Add the two parallel bases first, then multiply by height and divide by 2
When To Use
For trapezoids with two parallel sides
Formula
A = ½d₁d₂
Meaning
A = area, d₁ and d₂ = diagonals
Watch Out
This only works for rhombus — don't use for other quadrilaterals
When To Use
For rhombus when both diagonals are given
Section Title
Area Formulas
Important Facts
- Area units are always squared (cm², m², ft²)
- For composite shapes, break into familiar pieces and add/subtract areas
- Heron's formula for triangles: A = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
Key Definitions
Term
Area
Example
The floor space of a room
Definition
The amount of space inside a 2D shape
Term
Base
Example
The bottom edge of a triangle
Definition
The bottom side of a shape, perpendicular to height
Term
Height
Example
The vertical distance in a triangle from base to top vertex
Definition
The perpendicular distance from base to opposite side
Diagrams To Know
- Triangle with base and height marked
- Circle with radius marked
- Trapezoid with parallel sides and height labeled
Reactions Or Equations
Note
s is the semi-perimeter: s = (a+b+c)/2
Equation
A = √[s(s-a)(s-b)(s-c)]
Conditions
When triangle has three known sides but no clear height
Formulas
Formula
V = s³
Meaning
V = volume, s = side length
Watch Out
Cube the side length — it's to the third power
When To Use
For cubes when one side is given
Formula
V = lwh
Meaning
V = volume, l = length, w = width, h = height
Watch Out
Make sure all three dimensions are in the same units
When To Use
For rectangular prisms (boxes) when all dimensions are known
Formula
V = πr²h
Meaning
V = volume, r = radius, h = height
Watch Out
Don't forget to square the radius first
When To Use
For cylinders when radius and height are known
Formula
V = ⅓πr²h
Meaning
V = volume, r = radius, h = height
Watch Out
Don't forget the ⅓ factor — very common mistake
When To Use
For cones when radius and height are known
Formula
V = ⅓lwh
Meaning
V = volume, l = length, w = width, h = height
Watch Out
Don't forget the ⅓ factor for pyramids
When To Use
For pyramids with rectangular base
Formula
V = (4/3)πr³
Meaning
V = volume, r = radius
Watch Out
Cube the radius and remember the 4/3 coefficient
When To Use
For spheres when radius is given
Common Values
Value
1000 cm³
Symbol
L
Quantity
1 liter
Section Title
Volume Formulas
Important Facts
- Volume units are always cubed (cm³, m³, liters)
- Cones and pyramids always have ⅓ in their volume formulas
- 1 liter = 1000 cm³ = 0.001 m³
Key Definitions
Term
Volume
Example
The water that fits in a bottle
Definition
The amount of 3D space occupied by a solid
Term
Cylinder
Example
A can of soda
Definition
A solid with circular base and top connected by curved surface
Term
Cone
Example
An ice cream cone
Definition
A solid with circular base tapering to a point
Diagrams To Know
- Cylinder with radius and height labeled
- Cone with radius and height labeled
- Sphere with radius marked
Formulas
Formula
y = mx + b
Meaning
m = slope, b = y-intercept, (x,y) = any point on line
Watch Out
b is where line crosses y-axis, not x-axis
When To Use
When you know slope and y-intercept, or need to graph quickly
Formula
y - y₁ = m(x - x₁)
Meaning
m = slope, (x₁,y₁) = known point, (x,y) = any point on line
Watch Out
Use the coordinates of the KNOWN point for x₁ and y₁
When To Use
When you know one point and the slope
Formula
Ax + By = C
Meaning
A, B, C = constants, (x,y) = any point on line
Watch Out
To find x-intercept, set y = 0; for y-intercept, set x = 0
When To Use
Standard form — useful for finding intercepts
Formula
m = (y₂ - y₁)/(x₂ - x₁)
Meaning
m = slope, (x₁,y₁) and (x₂,y₂) = two points on line
Watch Out
Keep y-coordinates in numerator, x-coordinates in denominator
When To Use
When you have two points and need to find slope
Section Title
Equation of a Line
Important Facts
- Positive slope: line goes up from left to right
- Negative slope: line goes down from left to right
- Zero slope: horizontal line
- Undefined slope: vertical line
- Parallel lines: m₁ = m₂
- Perpendicular lines: m₁ × m₂ = -1
Key Definitions
Term
Slope
Example
A slope of 2 means up 2, right 1
Definition
The steepness of a line, rise over run
Term
Y-intercept
Example
Point (0, 3) means y-intercept is 3
Definition
Where the line crosses the y-axis (x = 0)
Term
Parallel lines
Example
Lines with slopes 2 and 2 are parallel
Definition
Lines with equal slopes that never intersect
Term
Perpendicular lines
Example
Slopes 2 and -½ are perpendicular
Definition
Lines whose slopes multiply to -1
Diagrams To Know
- Coordinate plane with line showing slope and y-intercept
- Two parallel lines with same slope
- Two perpendicular lines forming 90° angle
Reactions Or Equations
Note
One slope is negative reciprocal of the other
Equation
m₁ × m₂ = -1
Conditions
For perpendicular lines
Formulas
Formula
d = √[(x₂-x₁)² + (y₂-y₁)²]
Meaning
d = distance, (x₁,y₁) and (x₂,y₂) = two points
Watch Out
Don't forget to take the square root at the end
When To Use
To find distance between any two points
Formula
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Meaning
M = midpoint, (x₁,y₁) and (x₂,y₂) = endpoints
Watch Out
Add coordinates first, then divide by 2 for each coordinate
When To Use
To find the point exactly halfway between two points
Section Title
Distance and Midpoint
Important Facts
- Distance formula comes from Pythagorean theorem
- Distance is always positive
- Midpoint coordinates are averages of endpoint coordinates
Key Definitions
Term
Distance
Example
Distance from (0,0) to (3,4) is 5 units
Definition
The straight-line length between two points
Term
Midpoint
Example
Midpoint of (1,2) and (5,8) is (3,5)
Definition
The point exactly halfway between two other points
Diagrams To Know
- Two points connected by line segment with midpoint marked
- Right triangle showing distance formula derivation
Must Remember
- Area units are SQUARED, volume units are CUBED
- Cones and pyramids have ⅓ in volume formula
- For circles: C = 2πr, A = πr² (don't mix them up)
- Perpendicular slopes multiply to -1
- Slope = rise/run = (y₂-y₁)/(x₂-x₁)
- Triangle area: A = ½bh (height must be perpendicular to base)
- If given diameter, divide by 2 to get radius
- Parallel lines have equal slopes
- Distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²]
- For composite figures: break into simple shapes, then add/subtract
Last Minute Tips
- Draw and label diagrams — most mistakes come from using wrong measurements
- Check units — convert everything to same unit before calculating
- For word problems, identify the shape first, then choose the right formula
- When finding line equations, always identify what information you have (slope? points? intercepts?)
- For circle problems, check if you're given radius or diameter — don't assume!
Comparison Tables
Rows
Values
- 1D (length)
- cm, m, ft
- P = 2l + 2w
Property
Perimeter
Values
- 2D (surface)
- cm², m², ft²
- A = lw
Property
Area
Values
- 3D (space)
- cm³, m³, ft³
- V = lwh
Property
Volume
Columns
- Concept
- Dimension
- Units
- Example Formula
Table Title
Perimeter vs Area vs Volume
Rows
Values
- y = mx + b
- Graphing or slope/y-intercept given
Property
Slope-intercept
Values
- y - y₁ = m(x - x₁)
- One point and slope given
Property
Point-slope
Values
- Ax + By = C
- Finding intercepts
Property
Standard
Columns
- Form
- Equation
- Best Used When
Table Title
Line Forms Quick Reference
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