Answer:
Perimeter = 18.7 units
Area = 13.5 units²
Step-by-step explanation:
Perimeter of ADEC = AD + DE + EC + AC
Length of AD = 3 units
By applying Pythagoras theorem in ΔDBE,
DE² = DB² + BE²
DE² = 3² + 3²
DE = √18
DE = 4.24 units
Length of EC = 3 units
By applying Pythagoras theorem in ΔABC,
AC² = AB² + BC²
AC² = 6² + 6²
AC = √72
AC = 8.49 units
Perimeter of ADEC = 3 + 4.24 + 3 + 8.49
= 18.73 units
≈ 18.7 units
Area of ADEC = Area of ΔABC - Area of ΔBDE
Area of ΔABC = [tex]\frac{1}{2}(AB)(BC)[/tex]
= [tex]\frac{1}{2}(6)(6)[/tex]
= 18 units²
Area of ΔBDE = [tex]\frac{1}{2}(BD)(BE)[/tex]
= [tex]\frac{1}{2}(3)(3)[/tex]
= 4.5 units²
Area of ADEC = 18 - 4.5
= 13.5 units²
