Question

Construct a hexagon of side 4.5 cm and draw all its lines of symmetry.

Answer 1

Given: Construct a regular hexagon of side 4.5 cm and draw all its lines of symmetry.

Steps of construction:

Method 1 Using interior angles:

1. Draw a line segment AB = 4.5 cm.
2. At point A, construct an angle of 120° and mark point F such that AF = 4.5 cm.
3. At point B, construct an angle of 120° and mark point C such that BC = 4.5 cm.
4. Similarly, at points C, D, E and F, construct angles of 120° and mark points D, E and complete the hexagon such that each side is 4.5 cm.
5. Join all vertices to form the hexagon ABCDEF.

Method 2 Using circumcircle and radius:

1. Draw a circle with center O and radius 4.5 cm.
2. Mark any point A on the circumference.
3. With center A and radius 4.5 cm, cut the circle at points B and F.
4. With center B and radius 4.5 cm, cut the circle at C.
5. With center C and radius 4.5 cm, cut the circle at D.
6. With center D and radius 4.5 cm, cut the circle at E.
7. Join points A, B, C, D, E, F to form the regular hexagon.

Drawing lines of symmetry:

• A regular hexagon has 6 lines of symmetry.
• These lines of symmetry can be drawn by joining:
  • Opposite vertices for 3 lines
  • Midpoints of opposite sides for other 3 lines
• Therefore, draw straight lines connecting opposite vertices A to D, B to E, C to F.
• Also, draw lines joining midpoints of opposite sides.

The regular hexagon with side 4.5 cm is constructed using either side and interior angle method or circumcircle method. It has 6 lines of symmetry, drawn by joining opposite vertices and midpoints of opposite sides.