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
