Answer:
The perimeter is = 6(1 + √2) + 3π cm.
Total area = 4.5(4 + π) cm².
Step-by-step explanation:
The given figure is consists of an isosceles right triangle and a semi-circle.
Perimeter calculation :
AC is the hypotenuse and equal to = [tex]\sqrt{6^{2} + 6^{2}} = 6\sqrt{2}[/tex] cm.
AB = 6 cm and
Arc BC = πr = 3π {Since [tex]r = \frac{BC}{2} = \frac{6}{2} = 3[/tex] cm.}
Therefore, the perimeter is = 6 + 6√2 + 3π = 6(1 + √2) + 3π cm.
Area calculation :
Area of the triangle = [tex]\frac{1}{2} \times 6 \times 6 = 18[/tex] cm².
Area of the semi circle = [tex]\frac{1}{2}\pi r^{2} = \frac{1}{2}\pi (3)^{2} = 4.5\pi[/tex] cm²
Therefore, total area = 18 + 4.5π = 4.5(4 + π) cm². (Answer)
