Perimeter and area — Study Path Agent

Chapter 1

Core ideas, vocabulary, and units

1

Perimeter vs. area: what each measures (boundary length vs. surface)

2

Units: linear units vs. square units; why area units are “squared”

3

Common shapes and parts: side, base, height, radius, diameter

4

Measurement skills: using rulers/grid paper; estimating reasonableness

5

Scaling intuition: doubling lengths vs. how perimeter/area change

Chapter 2

Perimeter: formulas & strategies

6

Perimeter of polygons: add all side lengths (including irregular shapes)

7

Rectangle & square perimeter: P = 2(l + w), P = 4s

8

Triangle perimeter and special cases (equilateral/isosceles)

9

Circumference of circles: C = 2πr = πd (and using π approximations)

10

Finding unknown side lengths from patterns or given relationships

Chapter 3

Area: formulas & strategies

11

Area model: counting unit squares on a grid (build intuition)

12

Rectangle & square area: A = lw and A = s²

13

Parallelogram area: A = bh (why it works via rearrangement)

14

Triangle area: A = ½bh (including right triangles)

15

Trapezoid area: A = ½(b1 + b2)h

16

Circle area: A = πr² (and choosing π ≈ 3.14 or 22/7)

Chapter 4

Composite figures & missing measures

17

Composite area: split into known shapes, add/subtract areas

18

Composite perimeter: include only outer edges (avoid counting interior edges)

19

Missing side lengths: use opposite sides equal (rectangles/parallelograms) and shared sides

20

Using angle/right-angle cues to identify bases and heights correctly

21

Optimization intuition: same perimeter, different area (and vice versa)

Chapter 5

Coordinate geometry connections (optional but useful)

22

Distance on a grid for axis-aligned shapes (count squares and use differences)

23

Area on the coordinate plane for rectangles/triangles (counting + simple decomposition)

Chapter 6

Word problems, real-world applications, and checking work

24

Translate word problems into diagrams and labeled measurements

25

Unit conversion basics (e.g., cm↔m) and why area conversions square the factor

26

Multi-step problems: fencing vs. tiling; when to compute perimeter vs. area

27

Common mistakes checklist (mixing units, wrong height, counting inside edges)

28

Practice set: mixed perimeter/area problems with self-check (estimate + exact)