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##?

##A_Delta = 1/2 bxxh ~~ 5/ 2 (2.1xx3.23) ~~17##

Given: The side of the of the larger regular pentagon, ##s=5.5## Area smaller pentagon, ##A_(pentagon) = 7.59##

Required: Area of the yellow shaded triangles of the pentagram?

Solution Strategy: 1) Find ##theta and alpha## knowing we have a regular pentagon ##alpha = 180[(n-2)]/n## n is number of sides, ##n=5## ##alpha=180(3)/5=108^0, :. theta=72^0## 2) Find the side of the small pentagon knowing that, ##A_("small pentagon")=7.59## ##A_("small pentagon") = 1/4 sqrt(5(5+2sqrt(5) )) a^2## ##a = 25^(3/4) sqrt(A)/(5(sqrt20+5)^(1/4)) =25^(3/4) sqrt(7.59)/(5(sqrt20+5)^(1/4)) ~~ 2.1## 3) Find the altitude/height of the yellow triangle: ##tan72= (Opp)/(Adj)= h/(b/2); h=1.05tan(72) ~~ 3.23## 4) Area of the triangle and multiply by 5 ##A_Delta = 1/2 bxxh ~~ 5/ 2 (2.1xx3.23) ~~17##