MICRO LESSON 1
Why Another Formula?
Picture it:
Sometimes height is unknown but all sides are known.
Simple:
Heron’s formula uses three sides directly.
Example:
Land with sides measured but no altitude.
Quick Check:
What information is needed?
MICRO LESSON 2
Semi-Perimeter
Picture it:
Semi-perimeter is half the perimeter.
Simple:
s=(a+b+c)/2.
Example:
Sides 3,4,5 give s=6.
Quick Check:
Find s for 5,5,6.
MICRO LESSON 3
Heron’s Formula
Picture it:
Area=√[s(s-a)(s-b)(s-c)].
Simple:
Substitute sides carefully.
Example:
For 3,4,5: √(6×3×2×1)=6.
Quick Check:
What is written under root?
MICRO LESSON 4
Checking Triangle Validity
Picture it:
The sides must form a triangle.
Simple:
Any two sides must sum greater than third.
Example:
2,3,6 invalid.
Quick Check:
Can 4,4,8 form a triangle?
MICRO LESSON 5
Square Root Simplification
Picture it:
The product under the root may be a perfect square.
Simple:
Factor carefully.
Example:
√144=12.
Quick Check:
What is √225?
MICRO LESSON 6
Quadrilateral by Splitting
Picture it:
A diagonal can divide a quadrilateral into two triangles.
Simple:
Use Heron for each and add areas.
Example:
Irregular field split into triangles.
Quick Check:
Why add two areas?