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Diwali maths activities for Class 9 and Class 10

A ready-to-teach Diwali lesson built around rangoli patterns and diyas: a 5-minute starter, a 35-minute main activity, an extension and full worked answers.

Level
CBSE Class 9 and Class 10
Time
40 minutes, plus a 10-minute extension
Topics
Symmetry and reflections in the axes; Areas related to circles; Surface areas and volumes: hemisphere and cylinder; Angles of regular polygons and tessellation; Area of a triangle (Heron’s formula)
Equipment
No calculator. Every answer works out exactly; use π = 22/7 where a question says so.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A9 minA rangoli on a grid
Main: task B9 minA circular rangoli
Main: task C9 minThe diya
Main: task D8 minTiles for a rangoli floor
Extension10 minFast finishers or homework

Starter (5 minutes)

Quick-fire mental maths.

  1. How many lines of symmetry does a regular hexagon have?
  2. Find each interior angle of a regular octagon.
  3. Find the area of a circle of radius 7 cm. (Use π = 22/7.)
  4. Write down the reflection of the point (3, −5) in the x-axis.

Main activity (35 minutes)

Task A: A rangoli on a grid (9 min)

A rangoli is drawn on squared paper with its centre at the origin. Its outline joins A(2, 0), B(0, 2), C(−2, 0) and D(0, −2).

  1. Show that ABCD is a square.
  2. Find the area of ABCD.
  3. A petal of the rangoli has its tip at P(1, 3). The design is symmetric in both axes. Write down the tips of the other three petals, and find the area of the rectangle they form with P.

Task B: A circular rangoli (9 min)

A circular rangoli of radius 21 cm is divided into 8 equal sectors, coloured alternately. Use π = 22/7.

  1. Find the area of one sector.
  2. Find the length of the arc of one sector.
  3. The rangoli fits exactly inside a square of side 42 cm. Find the area of the square outside the circle.

Task C: The diya (9 min)

A diya is modelled as a hemispherical bowl of radius 3.5 cm. Use π = 22/7.

  1. Find the curved outer surface area to be painted.
  2. Find the volume of oil the diya holds when full.
  3. A cylindrical bottle of oil has radius 3.5 cm and height 12 cm. How many diyas can be filled completely?

Task D: Tiles for a rangoli floor (8 min)

A tessellation covers a floor with regular polygons, with no gaps or overlaps.

  1. Explain why regular pentagons cannot tessellate on their own.
  2. Show that two regular octagons and one square fit together exactly at a point.
  3. Two copies of a regular n-sided polygon and one equilateral triangle fit exactly at a point. Find n.

Extension (10 minutes)

For fast finishers, or as homework.

  1. A triangular section of a rangoli has sides 13 cm, 14 cm and 15 cm. Find its area.
  2. A rangoli outline is a regular polygon with 20 diagonals. How many sides does it have?

For teachers

Teacher notes and full worked answers
  • Invite students to design their own rangoli on squared paper with a stated number of lines of symmetry and order of rotational symmetry, then swap and check.
  • In the diya task, cancel 3.5 = 7/2 early: 22/7 × 7/2 × 7/2 keeps every step exact.
  • Tessellation links to Class 8 and 9 angle work; the last part is a good test of reasoning rather than recall.

Starter

  1. 6
    • A regular n-sided polygon has n lines of symmetry.
  2. 135°
    • Exterior angle = 360° ÷ 8 = 45°, so interior angle = 180° − 45° = 135°.
  3. 154 cm2
    • 22/7 × 7 × 7 = 154
  4. (3, 5)
    • Reflecting in the x-axis changes the sign of the y-coordinate.

Task A: A rangoli on a grid

  1. All sides 2√2 and both diagonals 4
    • AB = BC = CD = DA = √(22 + 22) = 2√2.
    • Diagonals AC = BD = 4. Equal sides and equal diagonals, so ABCD is a square.
  2. 8 square units
    • (2√2)2 = 8, or half the product of the diagonals: ½ × 4 × 4 = 8.
  3. (−1, 3), (1, −3), (−1, −3); area 12
    • Reflect in the y-axis: (−1, 3). In the x-axis: (1, −3). In both: (−1, −3).
    • The rectangle is 2 wide and 6 tall: area 12.

Task B: A circular rangoli

  1. 693/4 = 173.25 cm2
    • Whole circle: 22/7 × 21 × 21 = 1386 cm2.
    • One sector: 1386 ÷ 8 = 173.25 cm2.
  2. 16.5 cm
    • Circumference: 2 × 22/7 × 21 = 132 cm. One arc: 132 ÷ 8 = 16.5 cm.
  3. 378 cm2
    • 42 × 42 − 1386 = 1764 − 1386 = 378

Task C: The diya

  1. 77 cm2
    • 2 × 22/7 × 3.5 × 3.5 = 77
  2. 539/6 cm3 (89⅚ cm3)
    • 2⁄3 × 22/7 × 3.5 × 3.5 × 3.5 = 2⁄3 × 22/7 × 343/8 = 539/6
  3. 5 diyas
    • Bottle: 22/7 × 3.5 × 3.5 × 12 = 462 cm3.
    • 462 ÷ 539/6 = 2772/539 = 5 and a bit, so 5 full diyas.

Task D: Tiles for a rangoli floor

  1. 108° does not divide 360°
    • Each interior angle is 108°, and 360 ÷ 108 = 10/3 is not a whole number.
  2. 135° + 135° + 90° = 360°
    • Each octagon angle is 135° and the square’s is 90°: 135 + 135 + 90 = 360.
  3. n = 12
    • 2 × interior angle + 60° = 360°, so the interior angle is 150°.
    • Exterior angle = 30°, so n = 360 ÷ 30 = 12.

Extension

  1. 84 cm2
    • s = (13 + 14 + 15)/2 = 21.
    • Area = √(21 × 8 × 7 × 6) = √7056 = 84
  2. 8
    • A polygon with n sides has n(n − 3)/2 diagonals.
    • n(n − 3) = 40 gives n2 − 3n − 40 = 0, so (n − 8)(n + 5) = 0 and n = 8.

The same answers are in the answers PDF. Every answer was recomputed by computer before publishing.

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