Geometry Basics – Quick‑Study Guide
(AWS Certification – Quantitative Aptitude)
1. Simple Explanation
Geometry is the study of shape, size, position, and the properties of space. In quantitative aptitude, you’ll mainly need:
| Concept | What you’ll use it for |
|---|---|
| Lines & Angles | Solving problems on straight‑line relations and angle sums |
| Polygons | Finding perimeters, areas, and relationships between sides and angles |
| Circles | Working with radius, diameter, circumference, and area |
| Coordinate Geometry | Finding distances, midpoints, and slopes |
| Basic Transformations | Understanding symmetry, rotation, and reflection |
2. Key Points
| Category | Key Formula / Fact | Typical Question Type |
|---|---|---|
| Lines & Angles | • Sum of angles in a triangle = 180° • Sum of angles in a quadrilateral = 360° • Complementary: 90° • Supplementary: 180° |
“Angle D is ___ degrees. If angle E is 2× angle D, find angle E.” |
| Polygons | • Regular polygon: all sides & angles equal • Interior angle of n‑sided polygon = ((n-2)×180°/n) • Exterior angle = (360°/n) |
“A regular octagon has how many interior degrees?” |
| Perimeter / Area | • Rectangle: P = 2(l+w), A = l×w • Triangle: P = a+b+c, A = ½×base×height • Square: P = 4s, A = s² • Circle: Circumference = 2πr, Area = πr² |
“A rectangle has a perimeter of 48 cm and length 12 cm. Find width.” |
| Circles | • Diameter = 2r • Circumference = πd = 2πr • Area = πr² |
“A circle’s circumference is 31.4 cm. Find its area.” |
| Coordinate Geometry | • Distance (d = \sqrt{(x₂-x₁)^2+(y₂-y₁)^2}) • Midpoint (M = \left(\frac{x₁+x₂}{2}, \frac{y₁+y₂}{2}\right)) • Slope (m = \frac{y₂-y₁}{x₂-x₁}) |
“Points A(2,3) and B(8,11). Find the distance AB.” |
| Transformations | • Reflection: mirror image over a line • Rotation: turning shape around a point by a given angle • Translation: shifting shape by a vector |
“Rotate the triangle 90° clockwise about the origin.” |
3. Worked Example
Problem
A rectangle has a length of 15 cm. Its perimeter is 54 cm. Find the width and the area.
Step‑by‑Step Solution
-
Recall perimeter formula
[ P = 2(\text{length} + \text{width}) ] Plug in the known values: [ 54 = 2(15 + w) ] -
Solve for (w)
[ 54 = 30 + 2w \ 54 - 30 = 2w \ 24 = 2w \ w = 12 \text{ cm} ] -
Compute area
[ A = \text{length} \times \text{width} = 15 \times 12 = 180 \text{ cm}^2 ]
Answer
- Width: 12 cm
- Area: 180 cm²
4. Quick Revision Summary
| Topic | Formula / Rule | Quick Check |
|---|---|---|
| Triangle angles | Sum = 180° | Add three angles → 180° |
| Quadrilateral angles | Sum = 360° | Add four angles → 360° |
| Regular polygon interior | ((n-2)×180°/n) | 5‑gon = 108°, 6‑gon = 120° |
| Rectangle | P = 2(l+w), A = l×w | Double sum of sides → perimeter |
| Circle | Circumference = 2πr, Area = πr² | d = 2r, C = πd |
| Distance | (d = \sqrt{(Δx)^2+(Δy)^2}) | Use Pythagoras on Δx, Δy |
| Midpoint | (\left(\frac{x₁+x₂}{2},\frac{y₁+y₂}{2}\right)) | Average coordinates |
| Slope | (m = \frac{Δy}{Δx}) | Positive slope → rising line |
Tip: Always write down the formula first, then plug in the numbers. Double‑check units (cm, m, etc.) and remember that angles are in degrees.
Final Thought
Mastering these core geometry formulas gives you a solid base for the quantitative problems you’ll encounter in the AWS certification exam. Practice quick mental calculations for perimeters, areas, and simple coordinate distances—speed and accuracy go hand‑in‑hand in aptitude tests. Good luck!