MSU-SASE Mathematics — Perimeter, Area, Volume & Equation of a LineCheat Sheet
One-page cheat sheet for MSU-SASE Mathematics — Perimeter, Area, Volume & Equation of a Line. Every formula, definition, and key fact you need for this chapter, condensed to a single printable page. Designed for the final review session before the MSU-SASE 2026.
Exam context
On the MSU-SASE 2026, the Mathematics subtest carries a "Core" weight in Mindanao State University's pattern. Perimeter, Area, Volume & Equation of a Line lands at position 6th out of 9 in the standard review order. Target score is Competitive overall score, and roughly a meaningful share of items come from Mathematics on a typical MSU-SASE paper.
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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