Overview
This topic covers the properties of geometric shapes and how to measure distances, angles, and areas. You'll learn how to calculate perimeter, area, and volume, apply the Pythagorean theorem, and work with unit conversions and formulas for common figures like triangles, circles, and quadrilaterals.
Key Concepts and Structures
- Perimeter: The total distance around a shape. Sum all sides.
- Area Formulas:
- Rectangle:
A = l × w
- Triangle:
A = (1/2) × b × h
- Circle:
A = πr^2
- Volume Formulas:
- Rectangular prism:
V = l × w × h
- Cylinder:
V = πr^2h
- Pythagorean Theorem: For right triangles:
a^2 + b^2 = c^2
- Similarity: Similar figures have equal angles and proportional sides.
- Parallel and Perpendicular Lines:
- Parallel lines have the same slope.
- Perpendicular lines have negative reciprocal slopes.
- Circle Geometry:
- Circumference:
C = 2πr
- Central angle: angle formed at the center
- Inscribed angle: angle formed on the circle
- Sector area:
(θ / 360) × πr^2
- Unit Conversion: Convert between inches, feet, centimeters, etc. Use dimensional analysis to align units.
Step-by-Step Example
Problem: Find the area of a triangle with base 10 cm and height 6 cm.
Step 1: Use the triangle area formula:
A = (1/2) × b × h
Step 2: Plug in values:
A = (1/2) × 10 × 6 = 30
Final Answer: 30 cm²
Quick Tip
Memorize core area and volume formulas for common shapes. Label units in your work and double-check if your answer makes sense based on the figure.