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steposvetlana [31]
2 years ago
11

Need help please assist me find the area of a regular hexagon

Mathematics
1 answer:
garri49 [273]2 years ago
7 0

Answer:

The area of the regular hexagon is 166.3\ units^{2}

Step-by-step explanation:

we know that

The area of a regular hexagon can be divided into 6 equilateral triangles

so

step 1

Find the area of one equilateral triangle

A=\frac{1}{2}(b)(h)

we have

b=r=8\ units

h=4\sqrt{3}\ units ----> is the apothem

substitute

A=\frac{1}{2}(8)(4\sqrt{3})

A=16\sqrt{3}\ units^{2}

step 2

Find the area of 6 equilateral triangles

A=(6)16\sqrt{3}=96\sqrt{3}=166.3\ units^{2}

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Trying to factor by splitting the middle term

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The first term is,  12x2  its coefficient is  12 .

The middle term is,  +28x  its coefficient is  28 .

The last term, "the constant", is  +15

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Step-2 : Find two factors of  180  whose sum equals the coefficient of the middle term, which is   28 .

     -180    +    -1    =    -181

     -90    +    -2    =    -92

     -60    +    -3    =    -63

     -45    +    -4    =    -49

     -36    +    -5    =    -41

     -30    +    -6    =    -36

     -20    +    -9    =    -29

     -18    +    -10    =    -28

     -15    +    -12    =    -27

     -12    +    -15    =    -27

     -10    +    -18    =    -28

     -9    +    -20    =    -29

     -6    +    -30    =    -36

     -5    +    -36    =    -41

     -4    +    -45    =    -49

     -3    +    -60    =    -63

     -2    +    -90    =    -92

     -1    +    -180    =    -181

     1    +    180    =    181

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     4    +    45    =    49

     5    +    36    =    41

     6    +    30    =    36

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<u>Answer:</u> (-6x - 5) • (2x + 3)

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