Answer:
259.8 cm²
Step-by-step explanation:
Finding the side of the Hexagon
You can split the hexagon into two trapeziums. The height of each trapezium is 5√3 cm. To find the size of each side we need to form an equation using Pythagoras theorem, we can keep the side of the hexagon as x:
x² = (5√3)² + [tex](\frac{x}{2}) ^{2}[/tex]
x² = 75 + [tex]\frac{x^{2} }{4}[/tex]
[tex]\frac{3}{4} x^{2}[/tex] = 75
x² = 100
x = 10 cm
Finding the area
Now that we know the length of the side of the hexagon we can find it's area. So the equation to find the area of a trapezium is:
[tex]area = \frac{1}{2}(a+b)[/tex] × h
area = [tex]\frac{1}{2}[/tex](10 +20) × 5√3 - (20 as b because the line through the half of the hexagon is double the length of the side)
So the area of the trapezium is 75√3
And because there are two trapeziums in a hexagon we double the answer to get the area: 75√3 × 2 = 150√3
150√3 = 259.8 cm²
