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Shape and Space

Shape and Space. INTERNAL ANGLES. POLYGON (REGULAR). . A polygon is a two dimensional shape with straight sides. There are two types of polygon, regular and irregular. In a regular polygon each length and angle are equal. Below is a list of the first six regular polygons. Regular Hexagon.

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Shape and Space

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  1. Shape and Space INTERNAL ANGLES

  2. POLYGON (REGULAR) • . • A polygon is a two dimensional shape with straight sides. • There are two types of polygon, regular and irregular. • In a regular polygon each length and angle are equal. • Below is a list of the first six regular polygons Regular Hexagon Square Regular Pentagon Regular Heptagon Regular Octagon Equilateral Triangle

  3. INTERNAL ANGLES • What is the sum of internal angles in a square? • We can divide a square into two triangles • What is the sum of the internal angles of • triangle? • 180° • Two triangles in a square gives a total of • 2 × 180 = 360° • Size of one internal angle is 90° 90° 90° 90° 360 ÷ 4 = 90°

  4. INTERNAL ANGLES • What is the sum of internal angles in a pentagon? • We can divide a pentagon into three triangles • What is the sum of the internal angles of a triangle? • 180° • Three triangles in a pentagon gives a total of • 3 × 180 = 540° • Size of one internal angle is 108° 108° 108° 108° 108° 540 ÷ 5 = 108°

  5. INTERNAL ANGLES 180 ÷ 3 = 60° 180 × 1 = 180° 3 1 360 ÷ 4 = 90° 180 × 2 = 360° 2 4 3 540 ÷ 5 = 108° 5 180 × 3 = 540°

  6. EXERCISES • 1. Calculate the internal angle of a regular nonagon (9 sides). • 2. Calculate the internal angle of a regular decagon (10 sides). • 3. Calculate the internal angle of a regular hendecagon (11 sides). • 4. Calculate the internal angle of a regular dodecagon (12 sides). • What does the internal angle tend to when the number of sides increase?

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