THE TRANSITION LINE // FIELD NOTES // STOP 15
Triangle area, circle area, and prime factors
Field Book
Lessons 57 to 60
Method
Pencil and paper. Calculators never.
The survey crew borrows the yard: two area formulas, three lines each. The triangle takes half of base times height, the long order-of-operations chains settle one move per line, the circle's area rides pi at 3.14, and every composite number breaks all the way down to primes.
What you have to be able to do
- Find the area of a triangle
- Work long order-of-operations chains one line at a time
- Find the area of a circle
- Prime factor a composite number
The procedures
Area of a triangleField Book Lesson 57
- A_tri = 12 · B · H, worked on three lines.
Long chainsField Book Lesson 58
- Same four ranks as Stop 3, applied to longer expressions.
- Perform one operation per line, rewriting everything else.
Area of a circleField Book Lesson 59
- A_circ = π · r · r, with π taken as 3.14 from here on.
- Three lines: formula, substitution, answer.
Prime factorizationField Book Lesson 60
- Break each composite into two smaller factors and mark the primes as they appear.
- Read the finished answer from smallest prime to largest.
Worked: triangle floor
- A_tri = 12 · B · H
- = 12 · 10 · 7
- = 35 m2
Worked: factor 84
- 84 = 4 · 21 = 2 · 2 · 3 · 7
- Smallest to largest: 2 · 2 · 3 · 7.
Terms on the record
| Term | Meaning |
|---|
| area | the measure of the flat space a shape covers |
| base | the side a height stands on |
| height | the distance measured straight up from the base |
| prime factorization | a composite written entirely as a product of primes |