All of the triangles in the figure below are congruent. What is the area of the figure? Note that all measurements are in centimeters.

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OpenStudy (anonymous):

jimthompson5910 (jim_thompson5910):

What is the area of each triangle?

OpenStudy (anonymous):

4?

jimthompson5910 (jim_thompson5910):

yep
A = b*h/2
A = 4*2/2
A = 4

OpenStudy (anonymous):

A=1/2bh correct?

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jimthompson5910 (jim_thompson5910):

There are 6 of these triangles with the area of 4 square units, so the total area of the triangles combined is 6*4 = 24 square units

jimthompson5910 (jim_thompson5910):

so that takes care of the triangles

jimthompson5910 (jim_thompson5910):

for the hexagon, you start with this
|dw:1363123525779:dw|

jimthompson5910 (jim_thompson5910):

and you break it up like this
|dw:1363123556419:dw|
it's not the best drawing, but each triangle inside the hexagon is congruent and it's an equilateral triangle

OpenStudy (anonymous):

i got 72

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OpenStudy (anonymous):

i mean 96

OpenStudy (anonymous):

i accidentally split my hexagon up wrong

jimthompson5910 (jim_thompson5910):

the height of each triangle is 6 and the base is 4
|dw:1363123616908:dw|
so
A = b*h/2
A = 4*6/2
A = 12
There are 6 of these triangles, so the hexagon has a total area of 12*6 = 72 square units