Answer:
Area = (18 + 4.5π) cm²
Perimeter = (6√2 + 12 + 3π) cm
Step-by-step explanation:
The shaded region given is made up of triangle ABC and a semicircle
AB = BC = 6 cm (note that the triangle is a portion of a square)
Diameter of semi-circle (d) = BC = 6cm
Radius (r) = ½*6 = 3 cm
==>Area of the shaded region in terms of π
Area of shaded region = area of triangle + area of semicircle
Area = ½*a*b + ½*πr²
Area = ½*6*6 + ½*π3²
Area = 18 + ½*π9
Area = 18 + 4.5π
<em>Area of the shaded portion = (18 + 4.5π) cm²</em>
==>Perimeter of shaded region in terms of π
Perimeter of shaded region = perimeter of triangle + perimeter of semicircle
= Sum of all sides of the triangle + ½πd
Sides of triangles are AB = 6 cm, BC = 6 cm
Use Pythagorean theorem to find side AC:
AC² = AB² + BC²
AC² = 6² + 6² = 36 + 36 = 72
AC = √72 cm
Perimeter of shaded triangle = √72 + 6 + 6 = √72 + 12 = (6√2 + 12) cm
Perimeter of semicircle = ½*πd = ½π6
= 3π
<em>Perimeter of the whole shaded region in terms of π = (6√2 + 12 + 3π) cm</em>
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