How would I find the area of this hexagon?

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How would I find the area of this hexagon?

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Answer 1 · 2015-11-20T23:37:19

$30"cm"^2$

Explanation:

Consider the shapes the hexagon is cut into. There are two central squares and four congruent triangles.

Each squares area can be found through the formula $A=s^2$ . Both have sides $3$ so each square's area is $9$ . Since there are two squares, their total area is $18$ .

As for the triangles, $A=1/2bh$ .

Each triangle has $b=3$ and $h=2$ , so one of the triangle's areas is $1/2(3)(2)=3$ . There are four triangles, so their total area is $12$ .

We can add the total area of the squares ( $18$ ) and the triangles ( $12$ ) to find that the hexagon's total area is $30"cm"^2$ .

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How would I find the area of this hexagon?

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