💡 What You Will Learn
On the GED, perimeter problems often give you a shape's total perimeter and all but one side — you must find the missing side. When sides use mixed number fractions like 3⅝ or 4½, you need to add them carefully and subtract from the perimeter. This lesson walks through every skill you need!
The perimeter of a shape is the sum of all its side lengths. To find a missing side, subtract all the known sides from the total perimeter.
For any shape: P = side₁ + side₂ + side₃ + ... + sideₙ
Missing side = Perimeter − (sum of all other sides)
After subtracting, divide by 2 to find each x. x = (P − known sides) ÷ 2
P=15, sides 6¾ and 4⅛ are known.
x = 15 − 6¾ − 4⅛ = 4⅛
P=22½, length 8¼ is known.
2x = 22½ − 16½ = 6 → x = 3
| Shape | Formula | Notes |
|---|---|---|
| Triangle | P = a + b + c | 3 sides, all different |
| Rectangle | P = 2L + 2W | 2 pairs of equal sides |
| Pentagon | P = a+b+c+d+e | 5 sides total |
| Hexagon | P = a+b+c+d+e+f | 6 sides total |
| Any shape | x = P − known | Universal formula! |
If the shape has two equal missing sides (both labeled x), find their combined total first (P − known), then divide by 2 to get each one.
3⅝ means 3 + 5/8 | 4½ means 4 + 1/2
To add mixed numbers: convert to improper fractions, find a common denominator, add, then simplify.
3⅝ → (3×8+5)/8 = 29/8 4½ → (4×2+1)/2 = 9/2
LCD of 8 and 2 is 8.
9/2 = 36/8
29/8 + 36/8 = 65/8 = 8⅛
32 − 30¼ → 32 = 128/4 128/4 − 121/4 = 7/4 = 1¾
When adding fractions with unlike denominators:
½ and ⅛ → LCD = 8 → ½ = 4/8
¾ and ⅛ → LCD = 8 → ¾ = 6/8
Always find the least common denominator first!
Add every labeled side (with common denominators for fractions).
Example: 3⅝ + 4½ + 7 + 7 + 3⅝ + 4½ = 30¼
P − known sides = total of the x side(s)
Example: 32 − 30¼ = 1¾
Each x = 1¾ ÷ 2 = 7/8
If there's only 1 x side, stop at Step 2.
Perimeter: 32 → 32 − 30¼ = 1¾
Two x sides: 1¾ ÷ 2 = 7/8 cm ✅
Always add known sides first (Step 1), then subtract (Step 2), then divide if needed (Step 3). Never skip the order!
Before adding mixed fractions, convert all to the same denominator. 3⅝ and 4½ → LCD=8 → work in eighths throughout.
Some shapes have two sides labeled x. Find their total first, then divide by 2. Don't forget this step!
Write out all side values clearly. GED problems often give some sides without labels — read the diagram carefully!
If your answer is 7/4, write it as 1¾. GED answers are usually in mixed number form if greater than 1.
Plug x back in: known sides + x should equal the perimeter. If it doesn't match, you made an error somewhere.
Step 1: Add all known sides (get a common denominator first)
Step 2: x total = Perimeter − sum of known sides
Step 3: If 2 equal x sides → divide by 2