Polygons

Polygons and Quadrilaterals

Name polygons by side count: triangle to octagon.
Classify quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium.
Count diagonals in simple polygons (intro).

Shape	Key property
Square	4 equal sides, 4 right angles
Rectangle	Opposite sides equal, 4 right angles
Rhombus	4 equal sides, angles not necessarily 90°
Parallelogram	Opposite sides parallel and equal
Trapezium	One pair of parallel sides

A diagonal joins two non-adjacent vertices.

Regular polygon: all sides and all angles equal (e.g. equilateral triangle, square).

NCERT anchor: Math-Magic 4, Ch 11 — Fields and Fences; Ch 5 — The Way The World Looks (shapes from different views)

How many diagonals does a rectangle have?

Step 1 — Label corners A, B, C, D.
Step 2 — Diagonals: AC and BD.
Step 3 — No other non-adjacent pairs.
Answer: **2 diagonals**

Classify a shape with 4 equal sides but no right angle

Step 1 — 4 sides → quadrilateral.
Step 2 — All sides equal → **rhombus**.
Step 3 — If angles were 90°, it would be a square.

Mistake	Why it happens	Fix
Every quadrilateral is a rectangle	Ignoring side equality	A rhombus may have no right angles
Pentagon has 4 sides	Confusing name with number	Penta = 5 sides
Diagonals of a rectangle are always equal	True for rectangle but not all quads	True for rectangle/square; not for all trapeziums
Hexagon appears only in foreign shapes	Missing local examples	Beehive cells in Anita and the Honeybees are hexagons

How many sides in an octagon?
Name a quadrilateral with one pair of parallel sides.
How many diagonals in a square?
Stretch: A rangoli uses regular hexagons. How many sides do 5 such hexagons have in total? (30 — count sides separately, not shared edges)

Revision tip: Draw the quadrilateral family tree: square fits inside rhombus and rectangle — both inside parallelogram.

Open the Practice tab for graded questions on Polygons and Quadrilaterals.