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Answered

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What is the area of the regular hexagon shown below?

Answer in complete sentences and include all relevant calculations.

What Is The Area Of The Regular Hexagon Shown Below Answer In Complete Sentences And Include All Relevant Calculations class=

Sagot :

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Answer:

6381.4 cm²

Step-by-step explanation:

Applying,

A = n/2(a×h)................ Equation 1

Where A = Area of the regular polygon, n = number of sides of the polygon, a = length of one side of the polygon, h = length of the apothem

But,

a = 2htan∅.............. Equation 2

Where ∅ = angle substands at the center by the regular polygon.

∅ = 360/n.................... Equation 3

Substitute equation 3 into equation 2

a = 2htan(360/n)........... Equation 4

Substitute equation 4 into equation 1

A = n/2[2htan(360/n)×h).............. Equation 5

From the question,

Given: n = 6 side, h = 24.78 cm

Substitute these values into equation 5

A = 6/2[24.78×24.78×2×tan(360/6)]

A = 3[24.78×(24.78×2×tan60°)]

A = 6381.4 cm²

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