Answer:
A ≈ 269.81 cm²
Step-by-step explanation:
This shape is a hexagon (it has 6 sides) so let's use the formula for the area of a hexagon.
A = [tex]\frac{3\sqrt{3} }{2} s^{2}[/tex]
Where s is the length of the sides
Substitute:
A = [tex]\frac{3\sqrt{3} }{2} s^{2}[/tex]
A = [tex]\frac{3\sqrt{3} }{2} 10^{2}[/tex]
Solve:
A = [tex]\frac{3\sqrt{3} }{2} 10^{2}[/tex]
A = [tex]\frac{3\sqrt{3} }{2} 100[/tex]
Multiply the numerator:
A = [tex]\frac{3\sqrt{3} }{2} 100[/tex]
A ≈ [tex]\frac{5.12 }{2} 100[/tex]
(The numerator reflects a rounded number, but the actual calculations are exact)
Divide the fraction:
A ≈ [tex]\frac{5.12 }{2} 100[/tex]
A ≈ 2.6(100)
Multiply:
A ≈ 2.6(100)
A ≈ 269.81 cm²
Therefore, the area is approximately 269.82 cubic centimeters.
