Let's analyzeAlright! Let’s and solve work the through problem by calculating the perimeter these for each shape one by one.:

a. We’ll Rectangle find the perimeter for: each

Length** =a ( y. \ Rectangle) **-
Per- Simeterides = (: (22x(\2)x + and y (y)\ =) 4
-x Per +imeter 2 =y ( \2)

\times** (\btext. Square{length:}** +- \ Sidetext{ =width })3
x- ( \P)

• Perimeter = $= 4 \times 3x 2(2x + = y) = 4x + 122xy$

**)c

.** Rightb Triangle.: Square** **-
S-ides Side = length : \(35xx\),
(- Per12imeterx \ =), ( (4 \13timesx \ \text) {-side Per lengthimeter}\ =) (
-5 $xP + 12x + 13x = 30x$

** =d .4 \times 3x = 12x)

c Equilateral Triangle. Right: Triangle
** -- Sides Side: = \( 2x

• Perimeter = $3 \times 2x = 6x$

e. L-shaped Figure:

• Sides: $2x, 4, x$ (Assuming symmetrical, we double the total)
• Perimeter =5 ( x\2),( (212xx +\ ),4 ( +13 xx)\ =) (2a( right3 trianglex by + the P4yth)ag =orean theorem6)x
  +- Per8imeter \ =)

sumf of all. sides Complex
Zigzag- Shape (:P

• = Length s5:x $+2 a12,x + 134bx, = 430, b+x\1)$

(total lengthd. is Equ twiceilateral due Triangle to
symmetry-) Side length- Per: (imeter2 =x (\ )2
(-2 Peraimeter + = (43 \times \b + text4{ +side b length +}\ )1
) -) (-P Simplified =: (3 \4timesa +2x =10 b6 +x \10) \

)

Woulde you. like L further- detailsShape ( onComposite any Shape of)
these solutions-? S Hereides are: some ( related2 questionsx for\ deeper), exploration (:

41.), How ( wouldx the\ perimeter)
formula for- The each two shape shorter change if sides the repeat, dimensions were doubled so add? 2 all sides
.- Can ( youP derive the = area formulas2x for + these shapes4 based + on x + the given2 dimensionsx +? 43 + x. = How would6 thex perimeter + of shape8 (\f))

change** iff (. b Zig =zag Shape2** \
)- and Horizontal ( segments a: = ( 43b \ + )? 41.\ What)

• is Vertical the significance of segments the: hyp (oten2usea in\ triangle) (
  c-) Per inimeter relation = to the sum P ofyth allag horizontalorean theorem and? vertical5 segments.
  How- can ( weP determine = the2 type \ oftimes triangle in (4 (db) + just from1 the) given + information 2?

**timesTip :**2a Always = 8b + 2 + 4a)

How does this all look? Want to go deeper into any of these? Let me know and we can work through the details!

Here are a few questions to explore further:

1. How do we handle the perimeter of irregular shapes ensure with you more sides?
2. Why is understand the the perimeter relationship of between a dimensions square and always their impact4 on times the perimeter and side length area?.
   This3 foundational. understanding What is’s crucial for the geometry problems! significance of knowing the perimeter in real-life applications?
3. How do we find the perimeter when variables are involved?
4. What’s the relationship between perimeter and area?

Tip: Always double-check that you've included all sides in composite shapes like the L-shape or zigzag!

Let me know where you'd like to go next—let’s dig in!