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#?

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Answer 1 · 2016-05-08T03:05:03

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.