Answer:
A = (4.5π + 18) cm²
P = 3π + 6(1 + √2) cm
Step-by-step explanation:
Give figure is a composite structure of one semicircle and one right triangle.
Therefore, area of the figure = Area of the semicircle + Area of the triangle
Area of the given semicircle = [tex]\frac{1}{2}(\pi r^{2} )[/tex]
Here r = radius of the semicircle
Area of the semicircle = [tex]\frac{1}{2}(\pi )(3)^2[/tex] [Given : AB = BC]
= 4.5π cm²
Area of the triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(6)(6)[/tex]
= 18 cm²
Total area = 4.5π + 18
A = (4.5π + 18) cm²
Perimeter of the figure = Circumference of the semicircle + AB + AC
Circumference of the semicircle = πr
= 3π
AB = 6 cm
AC = [tex]\sqrt{(\text{AB})^2+(\text{BC})^2}[/tex]
= [tex]\sqrt{6^2+6^2}[/tex]
= [tex]6\sqrt{2}[/tex]
Perimeter 'P' = 3π + 6 + [tex]6\sqrt{2}[/tex]
= 3π + 6(1 + √2) cm
