Perimeter vs Area

Description

A rectangle is shown on screen. The perimeter is demonstrated by a dot walking around
all four sides while a counter adds up each side length. The area is then shown by
filling the interior with a grid of unit squares, one column at a time. Both results
are labeled with their standard formulas.

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Phases

#	Phase Name	Duration	Description
1	Title card	3 s	Title "Perimeter vs Area" fades in
2	Rectangle intro	3 s	Rectangle 5×3 drawn with side labels
3	Perimeter walk	10 s	Dot travels along all 4 sides; counter shows running total
4	Perimeter formula	4 s	Formula P = 2(l+w) = 2(5+3) = 16 shown
5	Clear & area intro	2 s	Transition text "Now let's find the Area!"
6	Area fill	8 s	5×3 = 15 unit squares fill the interior one column at a time
7	Area formula	4 s	Formula A = l×w = 5×3 = 15 shown
8	Both results	4 s	Both P and A shown side-by-side; fade out

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Layout

+--------------------------------------------------+
|            Perimeter vs Area                     |
|                                                  |
|        w = 3                                     |
|    +----------+      [counter: 0 → 16]           |
|  l=5|  (dot→) |                                  |
|    +----------+                                  |
|                                                  |
|   P = 2(l+w) = 16     A = l×w = 15              |
+--------------------------------------------------+

Area Descriptions

Area	Content	Notes
Top banner	Title	Large yellow text
Center	Rectangle outline (5 units × 3 u)	White stroke
Side labels	"l = 5", "w = 3"	White text next to sides
Walking dot	Green dot moving around perimeter	Smooth MoveAlongPath animation
Counter	Running total, e.g. "+ 5 = 5"	Cyan text top-right
Interior grid	Unit squares filling the rectangle	Blue fill, semi-transparent
Formula area	P and A formulas	Yellow MathTex

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Assets & Dependencies

• Fonts: LaTeX (MathTex), Manim default (Text)
• Colors: YELLOW (title/formulas), GREEN (perimeter dot), CYAN (counter), BLUE (area fill)
• Background: #1a1a2e
• Manim version: ManimCE 0.19.1

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Notes

• Rectangle is 5 units wide × 3 units tall, scaled to fit nicely on screen.
• Perimeter dot uses MoveAlongPath with a VMobject polygon path.
• Unit squares for area use Square objects in a nested loop, faded in column by column.
• Formula uses MathTex with highlight boxes around P and A.