# Find the area of a regular hexagon ( divided into 6 equilateral triangles) with side 8 cm.

2
by preet2002

2016-01-17T15:50:06+05:30
Length of each side of the equilateral triangle = 8 cm
Now, area of 1 equilateral triangle,
Semi-perimeter = (a + b + c)/ 2
S = 8 + 8 + 8 / 2
S = 24 / 2
S = 12 cm

By heron’s formula, Area = √s(s-a)(s-b)(s-c)
Area = √12 * 12-8 * 12-8 * 12-8
Area = √12 * 4 * 4 * 4
Area = √2 * 2 * 3 * 2 * 2 * 2 * 2 * 2 * 2
Area = 16√3 cm2
Therefore area of 6 such triangles, = 16√3 * 6 = 96√3cm2

therefore area of the regular hexagon = 96√3cm2

Thank You…………
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2016-01-17T15:53:52+05:30
Side of the hexagon = 8 cm

( In regular hexagon all sides are equal)

Given that it is divided into 6 equilateral triangle

Side of the triangle = 8 cm

Area of equilateral triangle = √3a²/4
= √3 × 8 ×8 /4
= 16√3 cm²

Given that there are 6 equilateral triangle = 16√3 ×6
= 96√3 cm²