Mathematics

Question

Can someone please help me?? Im not quite sure how to get this answer.

What is the area of the shaded region in the figure below? Leave answer in terms of pi and in simplest radical form.
Can someone please help me?? Im not quite sure how to get this answer. What is the area of the shaded region in the figure below? Leave answer in terms of pi an

1 Answer

  • Answer:

    C. 54π + 20.25√3 cm²

    Step-by-step explanation:

    The shaded area can be split into two areas: a sector and an isosceles triangle.

    Area of a sector is:

    A = (θ/360°) πr²

    where θ is the central angle and r is the radius.

    Area of an isosceles triangle can be found with SAS formula:

    A = ½ ab sin θ

    where a and b are two sides of a triangle and θ is the angle between them.

    In this case, r = a = b = 9 cm.  The central angle of the sector is 240°, and the vertex angle of the triangle is 120°.  Therefore, the total area is:

    A = (240°/360°) π (9 cm)² + ½ (9 cm) (9 cm) sin 120°

    A = 54π + 20.25√3 cm²

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