Given the radius of the regular hexagon, its area is approximately 42in².
Hence, option B) is the correct answer.
Given that;
Since a regular hexagon can be divided into six equal triangle, we will determine the area of a single triangle and then multiply the area by 6 to get the area of the regular hexagon.
Angle of one triangle in the regular hexagon = 360°/6 = 60°.
To determine the height, we divide the triangle into two equal half, making a right angled triangle with hypotenuse 4in, Base 4in/2 = 2in.
We find the perpendicular height using Pythagoras theorem
h = √( (4)² - (2)² )
h = √( 16 - 4 )
h = √( 12 )
h = √( 2² × 3 )
h = 2√3
Now, we determine the area of a single triangle.
Area = (1/2) × base × height
Area = 0.5 × 4 × 2√3
Area = (4√3)in²
Now, to get the area of the regular hexagon, we multiply the area of the triangle by 6
Area of regular hexagon = 6 × (4√3)in²
Area of regular hexagon = 24(√3)in²
Area of regular hexagon = 41.57in² ≈ 42in²
Given the radius of the regular hexagon, its area is approximately 42in².
Hence, option B) is the correct answer.
Learn more about regular hexagons here: https://brainly.com/question/10941428
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