Find the area of the yellow shaded area govern the larger pentagon side #s=5.5# and area of the smaller pentagon (green) #A_(pentagon) = 7.59 cm^2#?

Answer 1

Toral Area (yellow regions)#=16.98" "#square centimeters

There are three colors involved in the figure. The pink, blue, and the yellow.

There is a simple approach to this problem using Trigonometry and Geometry. Solve for the angles and sides first.

Angle #/_DLK=DKL=36^@# Angle #/_LED=LDE=72^@#

We can now compute for the sides LD and LE.

Using Sine Law #(LD)/(sin 36^@)=s/sin 108^@#
#LD=((5.5)*sin 36^@)/sin 108^@# #LD=3.3991869381243#

Now let us compute one yellow triangle:

Area one yellow triangle#=1/2*(LD)^2*sin /_DLE#
Area one yellow triangle#=1/2*(3.3991869381243)^2*sin 36^@#
Area one yellow triangle#=3.3957740728828#

Now, compute the total area of the 5 yellow triangles

Total Area (5 yellow triangles)#=5*(3.3957740728828)#
Total Area (5 yellow triangles)#=16.978870364414" "#square centimeters

God bless....I hope the explanation is useful.

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Answer 2

To find the area of the yellow shaded region, subtract the area of the smaller pentagon (green) from the area of the larger pentagon (yellow). Given that the side length of the larger pentagon is 5.5 cm and its area is A_yellow = 7.59 cm^2, you can use the formula for the area of a regular pentagon:

[A = \frac{5}{4} \times s^2 \times \frac{1}{\tan(\frac{\pi}{5})}]

Using this formula, you can find the area of the larger pentagon (yellow) as well. Then, subtract the area of the smaller pentagon (green) from the area of the larger pentagon to get the area of the yellow shaded region.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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