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Stage 3 · Core Geometry Skills
Missing Side Lengths
The GED often gives you a formula and asks you to find a missing measurement. The key skill is rearranging the formula — working backwards using inverse operations.
Most geometry problems on the GED give you an area, perimeter, volume, or surface area — and ask you to find a missing side. You can't just plug in numbers. You have to rearrange the formula first.
Examples you'll see on the GED:
• "The area of a triangle is 40 sq ft. The base is 8 ft. Find the height."
• "The circumference is 62.8 ft. Find the radius."
• "The volume is 360 cubic ft. The length and width are given. Find the height."
Formulas You'll Use
Triangle Area
A = ½ × b × h
Rectangle Perimeter
P = 2l + 2w
Circle Circumference
C = 2πr
Circle Area
A = πr²
Rectangular Prism Volume
V = l × w × h
Cylinder Volume
V = πr²h
Inverse Operations — The Core Skill
To find a missing value, undo what was done to it. Work backwards.
Ask yourself: what is happening to the missing variable?
• The missing variable is being multiplied by something → divide to undo it
• The missing variable is having something added to it → subtract to undo it
• The missing variable is being squared → take the square root to undo it
• The missing variable is being halved (multiplied by ½) → multiply by 2 to undo it
Worked Example — Find the Height of a Triangle
The area of a triangle is 40 sq ft. The base is 8 ft. Find the height.
→ Write the formula: A = ½ × b × h
→ Plug in what you know — A is 40, b is 8: 40 = ½ × 8 × h
→ Multiply ½ × 8 together to simplify the right side: 40 = 4h
→ h is being multiplied by 4 — divide both sides by 4 to undo that: h = 40 ÷ 4
h = 10 ft
Worked Example — Find the Radius from Circumference
The circumference of a circle is 62.8 ft. Find the radius. Use π ≈ 3.14.
→ Write the formula: C = 2πr
→ Plug in what you know — C is 62.8, π is 3.14: 62.8 = 2 × 3.14 × r
→ Multiply 2 × 3.14 together to make one number: 62.8 = 6.28r
→ r is being multiplied by 6.28 — divide both sides by 6.28 to undo that: r = 62.8 ÷ 6.28
r = 10 ft
🎯 Step Strategy — Use This Every Time
1.Write the formula — start here, every time
2.Substitute known values — plug in what you know
3.Identify the unknown — what variable is still there?
4.Use inverse operations — undo until the unknown is alone