5 & 1/3 pi - 8 sqrt 3
1) Find the location of one circle: A = pi * r^2 > A = 16 pi.
You are watching: Find the area of the shaded portion intersecting between the two circles.
2) Draw or imagine one more radius drawn with its endsuggest on the endpoint of the chord. This creates an equilateral triangle. This additionally means that each angle of the triangle has actually a meacertain of 60 levels. So, considering that the triangle is part of the sector, the meacertain of the sector"s arc is 60 degrees.
3) With this information, you have the right to discover out the area of the sector: carry out 60/360 = 1/6. Then multiply by the location of the circle:
1/6 * 16 pi = 2 & 2/3 pi. So the area of the sector is 2 & 2/3 pi.
4) Then discover the area of the equilateral triangle: A = 1/4 * s^2 * sqrt 3 > A = 4 sqrt 3. So the area of the triangle is 4 sqrt 3.
5) Finally, discover the location of the segment or one of the shaded components. You would certainly carry out this by doing the location of the sector minus the location of the triangle > 2 & 2/3 pi - 4 sqrt 3. You also must multiply this by 2 since tright here are 2 segments that are component of the shaded percent. So your last exact answer would certainly be: 5 & 1/3 pi - 8 sqrt 3. The approximate answer would be 2.90.
Hope this helps! :)
Answer from: DIGlBICK9402
A=16/3 pi - 8Г3
Answer from: rhettnyah
Area shaded percent = 16/3 π - 8√3
The shaded percentage consists of 2 equal segment
∵ Two circles have the very same radii = 4
∵ The the size of the prevalent chord of the 2 circles = 4
∴ The central angle of each segment = π/3 (60° equilateral Δ)
∵ Area segment = area sector - area Δ
∵ Area sector = 1/2 r²Ф = 1/2 × (4)² × π/3 = 8/3 π
∵ Area Δ = 1/4 s² √3 = 1/4 × (4)² × √3 = 4√3
∴ Area segment = 8/3 π - 4√3
∴ Area shaded percentage = 2(8/3 π - 4√3) = 16/3 π - 8√3
Join other finish of chord from the center of 2 circles.
As these two circles are concentric circles .
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And the triangles are equilateral triangle.
Area of sector
Area of equilateral triangle having actually side 4 cm=
Area of area I = Area of sector - Area of equilateral triangle having actually side 4 cm
Area of colored area = 2 × Area of area I
= 2 × 1.461
= 2.922 cm² (Approx)
Answer from: kierraware04
Are you going to include a picture for us to see?
Answer from: TH3L0N3W0LF
Look at the photo.ΔABC and ΔBDC are equilateral triangles.Area of sector of a circle:
So let"s try to discover the part of it in one circle then multiply it by 2.if the vertical line of shaded reason is 4, then 2 would certainly form a rt triangle with radius. thus the cos € = 2/4 = 1/2, so € = arccos (1/2)€ = 60°, and also 2× that = 120°so now one component of the shaded region is the entirety sector (pi×r^2) - the triangle within (base×ht):