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2 years ago

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

Mathematics

1 answer:

S_A_V [24]2 years ago

8 0

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.

<h3>3/4 circle area</h3>

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

<h3>Triangle area</h3>

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

A = 1/2s²

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

<h3>Shaded area</h3>

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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