OpenOlympiad
…
Concept 10 of 10Foundation
Video

📌 Formula Sheet — Perimeter and Area

Every formula with its derivation — so you NEVER forget which is which.

Perimeter of square: P = 4 × s
Means: s = side lengthUse when: fencing a square plot
Why: A square has 4 equal sides. Walk around once: s + s + s + s = 4s.
⚠ Trap: Perimeter uses length units (cm, m). No "squared" at the end.
Area of square: A = s²
Means: s = side lengthUse when: tiles on a square floor
Why: A square of side s fits s rows × s columns = s² unit squares.
⚠ Trap: If side doubles, area becomes 4× (not 2×). If side triples, area becomes 9×.
Perimeter of rectangle: P = 2(ℓ + b)
Means: ℓ = length, b = breadthUse when: fencing a rectangular plot
Why: Two lengths on top & bottom, two breadths on sides. Total = ℓ + ℓ + b + b = 2(ℓ + b).
⚠ Trap: Watch units! If ℓ in m and b in cm, convert first.
Area of rectangle: A = ℓ × b
Means: ℓ = length, b = breadthUse when: tiling, carpeting, painting
Why: A rectangle fits ℓ rows × b columns (or vice versa) of 1×1 unit squares. Total count = ℓ · b.
⚠ Trap: A square is a special rectangle — the formula ℓ×b becomes s×s = s².
Area of triangle: A = ½ × base × height
Means: base = any chosen side; height = perpendicular distance from opposite vertexUse when: computing triangle area
Why: Draw a rectangle around the triangle with same base and height. The triangle is exactly HALF of that rectangle. So A = ½ × (base × height).
⚠ Trap: Height must be PERPENDICULAR to the chosen base — NOT the slanted side.
Area of parallelogram: A = base × height
Means: same as rectangleUse when: slanted-sided figure
Why: Cut a triangle off one end of a parallelogram and slide it to the other end — you get a rectangle of the same base and height.
⚠ Trap: Don't use the slanted side as height.
Circle: Circumference C = 2πr; Area A = πr²
Means: r = radius, π ≈ 22/7 or 3.14Use when: any round shape — wheel, coin, plate, track
Why C = 2πr: π is DEFINED as C ÷ d. So C = π × d = π × (2r) = 2πr.
Why A = πr²: Cut a circle into many thin wedges and rearrange them into a near-rectangle of length πr (half the circumference) and height r. Area = πr × r = πr².
⚠ Trap: In area, the radius is SQUARED. Double the radius → area becomes 4×, not 2×.
Rhombus: Area = ½ × d₁ × d₂
Means: d₁, d₂ are the two diagonalsUse when: kite-ish shape with 4 equal sides
Why: Diagonals of a rhombus cross at right angles, splitting it into 4 right triangles with legs d₁/2 and d₂/2. Their areas sum to ½·d₁·d₂.
⚠ Trap: "base × height" also works if you know those, but diagonals are usually given.
Trapezium: Area = ½ × (a + b) × h
Means: a, b = lengths of the two parallel sides; h = perpendicular distance between themUse when: exactly one pair of parallel sides
Why: A trapezium's average 'width' is the average of the two parallel sides = (a+b)/2. Area = average width × height.
⚠ Trap: h must be PERPENDICULAR to the parallel sides — not the slant side.
Cube: Surface area = 6s²; Volume = s³
Means: s = side of cubeUse when: boxes with all equal sides (Rubik's cube, dice)
Why SA: A cube has 6 identical square faces, each of area s². Volume = length × breadth × height, and all three are s.
⚠ Trap: Volume unit is CUBIC (cm³, m³), not squared.
Cuboid: Surface area = 2(ℓb + bh + hℓ); Volume = ℓ × b × h
Means: ℓ, b, h are length, breadth, heightUse when: a brick, a book, a room
Why SA: A cuboid has 3 PAIRS of opposite faces: top/bottom (ℓ×b each), front/back (ℓ×h each), left/right (b×h each). Double the sum.
⚠ Trap: 1 litre = 1000 cm³ exactly. Useful in volume problems.
Unit conversions: 1 m² = 10,000 cm²; 1 hectare = 10,000 m²; 1 km² = 1,000,000 m²; 1 m³ = 1,000,000 cm³ = 1000 L
Rule: when converting AREA, square the length factor; for VOLUME, cube itUse when: switching units in word problems
Why: 1 m = 100 cm. 1 m² = (100)² cm² = 10,000 cm². 1 m³ = (100)³ cm³ = 1,000,000 cm³.
⚠ Trap: Don't just multiply by 100. Square it for area, cube it for volume.
💡 Tip:Perimeter = length (cm). Area = squared (cm²). Volume = cubed (cm³). The exponent reveals the dimension.
▶Prefer a video? Open YouTube search for “perimeter area volume formulas revision class 6”↗