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What is the area of the hexagon?

 

 Mar 17, 2021
 #1
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We put lies from the top line to the bottom line to make a side height of 8, we then find that the height of the small triangles are 2.14, 

 

we know the height and base of two triangles, and the area of the rectangle in the middle, the answer is known!

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 Mar 17, 2021
 #2
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let's draw a rectangle around the shape.

 

the area of the hexagon would be the area of the rectangle minus the areas of the small right triangles.

 

let's solve for the area of the rectangle first. this would just be 9.28 * 8 = 74.24.

 

now, let's do the area of the triangles. i believe the base of one triangle would be \(\frac{9.28-5}{2} = \frac{4.28}2 = 2.14\), and the height would just be 8/2 = 4.

 

to find the area of one triangle, we do \(\frac{2.14 \cdot 4}2\) = \(\frac{8.56}2\) = \(4.28\).

 

so the area of four of these triangles would be 4.28 * 4 = 17.12.

 

now we can solve the area of the hexagon - 

 

74.24 - 17.12 = 57.12.

 

hope this helped! please let me know if you are confused about anything i did :)

 Mar 17, 2021
edited by idyllic  Mar 17, 2021

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