http://www.ck12.org Chapter 10. Perimeter and Area
- Find the area of the blue sector of
⊙
A.Answers:
- Plug in what you know to the sector area formula and solve forr.
135 π=216 ◦
360 ◦
·πr^2135 =3
5
·r^2
5
3
· 135 =r^2225 =r^2 →r=√
225 = 15
- The radius of the circle is 16, which is also half of the diagonal of the square. So, the diagonal is 32 and the sides
would be√^32
2
·
√
√^2
2
= 16
√
2 because each half of a square is a 45-45-90 triangle.Acircle= 162 π= 256 πAsquare=(
16
√
2
) 2
= 256 · 2 = 512
The area of the shaded region is 256π− 512 ≈ 292. 25
- The right angle tells us that this sector represents^14 of the circle. The area of the whole circle isA=π 82 = 64 π.
So, the area of the sector is^1464 π= 16 π.
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Find the area of the blue sector or segment in
⊙
A. Leave your answers in terms ofπ. You may use decimals or
fractions in your answers, but do not round.