Measurement and Geometry Basics for the CSE: Formulas You Need

Measurement and basic geometry appear in the Numerical Ability section of the Civil Service Exam inside word problems and basic operations: the area of a lot, the number of tiles for a floor, a speed in metres per second, or the change from a payment. You need only a small set of formulas, but you must know them without a reference sheet. This guide collects them with worked examples.

Perimeter and area

Shape	Perimeter	Area
Rectangle (length l, width w)	2(l + w)	l × w
Square (side s)	4s	s²
Triangle (base b, height h)	sum of the three sides	½ × b × h
Circle (radius r)	2πr (circumference)	πr²

Examples

• A lot 12 m by 8 m: perimeter = 2 × (12 + 8) = 40 m; area = 12 × 8 = 96 m².
• A triangle with base 10 cm and height 6 cm: area = ½ × 10 × 6 = 30 cm².
• A circle with radius 7 cm, using π = 22/7: area = 22/7 × 7 × 7 = 154 cm².
• A circle with radius 14 cm: circumference = 2 × 22/7 × 14 = 88 cm.

Trap: perimeter and area are different. Perimeter is a length (m); area is a surface (m²). Exam options often include both.

Tip: when the radius is a multiple of 7, use π = 22/7 so the 7 cancels. When it is not, π ≈ 3.14 is usually intended.

Working back from area

A square has an area of 81 m². Its side is √81 = 9 m, so its perimeter is 4 × 9 = 36 m.

Volume

Solid	Volume
Rectangular box	l × w × h
Cube (side s)	s³
Cylinder	πr²h

A box 5 cm × 4 cm × 3 cm has a volume of 60 cm³.

Covering an area: tiles and similar problems

A room 4 m × 3 m is covered with tiles 0.5 m × 0.5 m. Floor area = 12 m²; tile area = 0.25 m²; tiles = 12 ÷ 0.25 = 48. Or: 4 ÷ 0.5 = 8 tiles along the length, 3 ÷ 0.5 = 6 along the width, 8 × 6 = 48.

The second method is often easier and avoids decimals.

Angles

• The angles of a triangle add up to 180°.
• The angles on a straight line add up to 180°; around a point, 360°.
• The interior angles of a polygon with n sides add up to (n − 2) × 180°.
  • Quadrilateral: 360°; pentagon: 540°; hexagon: 720°.
• Each exterior angle of a regular polygon = 360° ÷ n.

Two angles of a triangle are 50° and 60°, so the third is 180° − 110° = 70°.

Right triangles

The Pythagorean theorem: in a right triangle with legs a and b and hypotenuse c, a² + b² = c².

Legs 6 m and 8 m: c² = 36 + 64 = 100, so c = 10 m.

Know the common triples: 3-4-5, 5-12-13, 8-15-17, and their multiples (6-8-10, 9-12-15).

Conversions

Conversion	Rule
1 km = 1,000 m; 1 m = 100 cm; 1 cm = 10 mm	×1,000, ×100, ×10 going smaller
1 kg = 1,000 g	2.75 kg = 2,750 g
1 L = 1,000 mL	1,500 mL = 1.5 L
1 hour = 60 minutes	3.5 hours = 210 minutes
km/h to m/s	multiply by 5/18
m/s to km/h	multiply by 18/5

90 km/h × 5/18 = 25 m/s.

Rule of thumb: going from a larger unit to a smaller one, multiply; going from smaller to larger, divide.

Trap: 3.5 hours is 3 hours 30 minutes, not 3 hours 50 minutes.

Time

A meeting starts at 9:45 a.m. and lasts 2 hours 30 minutes. 9:45 + 2 h = 11:45; + 15 min = 12:00 noon; + 15 min = 12:15 p.m.

Add hours first, then minutes, and cross the hour in two steps.

Money

• Change: count up from the price. From ₱347 to ₱500: ₱3 to ₱350, then ₱150 to ₱500, so the change is ₱153.
• Unit price: 3 folders for ₱45 means ₱15 each, so 12 folders cost ₱180.
• Bills: ₱1,000 ÷ ₱20 = 50 bills.

Average speed

Average speed = total distance ÷ total time. 120 km in 2.5 h → 120 ÷ 2.5 = 48 km/h (double both: 240 ÷ 5).

Practise

Write each formula on a card and test yourself until you can state it instantly. Then work through our measurement, geometry and money set, where every answer was calculated and checked by script, and apply the same formulas in numerical word problems.