Question

ABCDEF us a regular hexagon of side 6cm . What is the area of triangle BDF?

Answer 1

Area of Triangle BDF = (1/2) Area of ABCDEF

Answer 2

Answer:

Area of ΔBDF  = 27√3 cm²

Step-by-step explanation:

Regular polygon:

• A polygon that has all the sides and all the interior angles equal is called a Regular polygon.
• Some of the examples of Regular polygons are Square, Rhombus, Equilateral triangle.

Given ABCDEF is a regular hexagon with a side of 6cm.

  We need to find the area of triangle BDF.

  From the figure, we can say that

Area of ΔBDF = (1/2)Area of Hexagon ABCDEF

Now first we need to find the Area of Hexagon ABCDEF.

Area of Hexagon ABCDEF = 6 x Area of Δ AOF

                                             = 6(√3/4)a²            (since side a = 6cm)

                                             = 6(√3/4)6x6

                                             =54√3 cm²

  Now, Area of ΔBDF = (1/2)Area of Hexagon ABCDEF

                                    = (1/2) (54√3)

          Area of ΔBDF  = 27√3 cm²

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