Area and Perimeter — Clear Definitions and Examples
Learn the difference between area and perimeter with formulas, worked rectangle and triangle examples, and practice links.
Perimeter vs area
Perimeter is the distance around a shape — fence length. Area is the space inside — grass to cover. Mixing them is the most common early geometry mistake.
Rectangle formulas
Perimeter of a rectangle: P = 2(L + W). Area: A = L × W. Units: perimeter in length units (cm, m); area in square units (cm², m²).
Worked example: rectangle
A garden is 8 m long and 5 m wide. Perimeter = 2(8 + 5) = 26 m of fencing. Area = 8 × 5 = 40 m² of sod. Same numbers, different questions, different units.
Triangle area
A = (1/2) × base × height. Height must be perpendicular to the base. Example: base 10 cm, height 6 cm → A = 30 cm².
Circle preview
Circumference (perimeter analog) C = 2Ï€r. Area A = Ï€r². Use the Area of Circle calculator after you attempt the substitution yourself.
Compound shapes
Split L-shapes into rectangles, find each area, then add. For perimeter, carefully include only outer edges — do not add internal cuts.
Word-problem tips
Highlight whether the story asks for fencing/border (perimeter) or covering/painting (area). Draw a quick sketch and label lengths before choosing a formula.
Practice on MathDigits
Open geometry worksheets by grade, use Area of Rectangle / Triangle / Circle calculators to verify, and browse the Formula Library for clean formula pages with examples. ## Units and unit conversion
If length is in centimetres, area is in square centimetres. Mixing metres of fencing with square centimetres of sod is a category error. Convert units before multiplying when a problem mixes them.
Squares and parallelograms
Square: perimeter equals 4s, area equals s squared. Parallelogram area equals base times perpendicular height, not the slant side. Students often multiply by the slant edge and overstate area.
Surface area preview
Surface area sums the areas of faces of a 3D shape. Volume measures capacity. Grade 5 volume of rectangular prisms (length times width times height) builds on area of the base. Keep vocabulary sharp so formulas do not blur.
Real-world project idea
Measure a tabletop, compute area for a cover, and perimeter for decorative trim. Bring numbers into MathDigits calculators only to check. Hands-on measurement makes abstract formulas stick.
Problem-solving checklist
Sketch. Label. Choose perimeter versus area. Write formula. Substitute. Units. Estimate. Check. That checklist beats guessing which button to press on a calculator. ## Mixed quiz
1) Rectangle 9 by 4: perimeter and area. 2) Triangle base 8 height 5: area. 3) Circle radius 3: approximate area with π = 3.14. Check with the matching MathDigits calculators after you finish.
Practice next
Turn this lesson into reps — play a game, open a worksheet, or drill a timed quiz.
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What is the difference between area and perimeter?
Perimeter measures the distance around a shape. Area measures the space inside, in square units.
What is the area of a rectangle?
Area = length × width. Always use square units such as cm² or m².
How do I find the area of a triangle?
Area = (1/2) × base × height, where height is perpendicular to the chosen base.