Answer:
Area of the shaded region = 51 cm²
Step-by-step explanation:
Area of the smaller pentagon ABKHG = 17 cm²
Since, B is the midpoint of side AC,
Scale factor used to enlarge the sides = [tex]\frac{\text{Measure of side AC}}{\text{Measure of side AB}}[/tex]
= [tex]\frac{AC}{\frac{AC}{2}}[/tex]
= 2
Therefore, area scale factor of both the pentagons = (Dimensional scale factor)²
2² = [tex]\frac{\text{Area of AFEDC}}{\text{Area of ABKHG}}[/tex]
4 = [tex]\frac{\text{Area of AFEDC}}{17}[/tex]
Area of bigger pentagon AFEDC = 4 × 17
= 68 cm²
Area of the shaded region = Area of the bigger pentagon - Area of the smaller pentagon
= 68 - 17
= 51 cm²
