# 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?

Toral Area (yellow regions)$= 16.98 \text{ }$square centimeters

#### Explanation:

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 $\angle D L K = D K L = {36}^{\circ}$
Angle $\angle L E D = L D E = {72}^{\circ}$

We can now compute for the sides LD and LE.

Using Sine Law
$\frac{L D}{\sin {36}^{\circ}} = \frac{s}{\sin} {108}^{\circ}$

$L D = \frac{\left(5.5\right) \cdot \sin {36}^{\circ}}{\sin} {108}^{\circ}$
$L D = 3.3991869381243$

Now let us compute one yellow triangle:

Area one yellow triangle$= \frac{1}{2} \cdot {\left(L D\right)}^{2} \cdot \sin \angle D L E$

Area one yellow triangle$= \frac{1}{2} \cdot {\left(3.3991869381243\right)}^{2} \cdot \sin {36}^{\circ}$

Area one yellow triangle$= 3.3957740728828$

Now, compute the total area of the 5 yellow triangles

Total Area (5 yellow triangles)$= 5 \cdot \left(3.3957740728828\right)$

Total Area (5 yellow triangles)$= 16.978870364414 \text{ }$square centimeters

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