Question

Find the area of the figure given to the right. The hexagon is regular. Round to the nearest whole number.

Answer 1

We can divide the hexagon into 6 equilateral triangles, and call the side 'x'. I will draw the situation:

Every line is x because the hexagon is regular (all sides have the same length). Therefore we can find x, because two times x is 18'':

`2x\text{ = 18}`
`x\text{ = 9 inches}`

The hexagon has the same area of 6 equilateral triangles with the side equal to x. The formula of the area of an equilateral triangle is:

`Area\text{ = }\frac{x^2\sqrt[]{3}}{4}`

Therefore the area of the hexagon will be:

`\text{AreaHexagon = 6}*\frac{x^2\sqrt[]{3}}{4}^{}`
`\text{AreaHexagon = 6}*\frac{9^2\sqrt[]{3}}{4}^{}`
`\text{AreaHexagon }\cong210.44\text{ square inches}`

Rounding it will be 210 square inches.