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find the area of the shaded region of circle y below. Round your answer to the nearest tenth if necessary

Find The Area Of The Shaded Region Of Circle Y Below Round Your Answer To The Nearest Tenth If Necessary class=

Sagot :

sqdancefan

Answer:

  285.6 square units

Step-by-step explanation:

The shaded area can be described a a whole circle less a 90° segment, or as a 3/4 circle with a right triangle added. The formula for the segment area is that of a sector less the triangle, so the computation is the same either way.

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3/4 circle area

The area of a circle is given by ...

  A = πr²

so 3/4 of a circle is 3/4 this value:

  3/4 circle area = (3/4)(π)(10²) = 75π . . . . square units

Triangle area

The area of the isosceles right triangle is given by ...

  A = 1/2s²

  A = 1/2(10²) = 50 . . . . square units

Shaded area

The shaded area is the sum of these two ...

  shaded area = 3/4 circle area + right triangle area

  shaded area = 75π + 50 ≈ 285.6 . . . . square units

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