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Ответ:

21hendlill

19.01.2022

3) 55.2 in^2

4) 42 yd^2

Step-by-step explanation:

The regular hexagon can be seen as consisting of 6 identical triangles, so its area is equal to six times the area of one triangle:

A=6A_T

The area of one triangle can be written as:

$A_T=\frac{1}{2}bh$

where:

b=4.6 in is the base of the triangle

h=4 in is the height

Substituting,

$A_T=\frac{1}{2}(4.6)(4)=9.2 in^2$

And so, the area of the regular hexagon is:

A=6A_T=6(9.2)=55.2 in^2

Here we have a complex figure consisting of several regular figures.

We observe that the figure consists of 2 parallelograms, on top and on bottom, so the total area of the figure is the sum of the areas of the two parallelograms:

A=2A_p

where A_p is the area of one parallelogram, which is given by

A_p = bh

where:

b = 7 yd is the base of the parallelogram

h = 3 yd is the height of the parallelogram

Therefore, the area of the parallelogram is

A_p=(7)(3)=21 yd^2

And therefore, the area of the figure is:

A=2A_p=2(21)=42 yd^2

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