Grade 4 (age 9-10)

Polygons

A polygon is a shape enclosed only by straight line segments. It is named by its number of sides, like a pentagon or hexagon, and if every side and angle is equal it is a regular polygon. You can find polygons all around you, in soccer balls and honeycombs. Here you can change the number of sides, split a polygon into triangles to find its angle sum, and count its diagonals.

What is a polygon?

🔷 A Shape Enclosed by Line Segments

①A polygon is a closed shape made only of straight lines

②By number of sides: triangle, quadrilateral, pentagon, ...

③If all sides and angles are equal, it's a regular polygon!

Explore Regular Polygons

Number of sides5

Interior Angle Sum from Triangles!

💡 Finding the Interior Angle Sum

①Drawing diagonals from one vertex splits it into triangles

②Number of triangles = sides - 2

③Sum of angles = (sides - 2) × 180°

Summary

Sum of Interior Angles

(n - 2) × 180°

Sum for an n-gon (triangle-splitting principle)

Each Angle (Regular)

(n - 2) × 180°n

Divide the sum by number of sides

Number of Diagonals

n(n - 3)2

Diagonals of an n-gon (n-3 from each vertex)

🎯 Key Points

①Polygon = closed shape of straight lines

②Regular polygon = all sides and angles equal

③Sum = (sides - 2) × 180°

④More sides → closer to a circle

⑤Diagonal count is computed from sides

Examples and Unit Test

Example 1

What is the sum of interior angles of a pentagon (5 sides)?

The interior angle sum formula is (sides − 2) × 180°.

(5 − 2) × 180° = 3 × 180° = 540°.

▸ 540°

Drawing diagonals from one vertex splits it into (sides − 2) triangles.

Example 2

What is each interior angle of an equilateral triangle?

A triangle's angle sum is (3 − 2) × 180° = 180°.

An equilateral triangle has three equal angles: 180 ÷ 3 = 60°.

▸ 60°

Each angle of a regular polygon = angle sum ÷ number of sides.

Unit Test

What is the sum of interior angles of a quadrilateral (4 sides)?

①180°

②360°

③540°

④720°

▸ ② 360°

Put 4 sides into (sides − 2) × 180°.

(4 − 2) × 180° = 2 × 180° = 360°.

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Quadrilateral Types

Plane Figure Movement