Lee Han Min's answer to LZmath's Secondary 3 E Maths Singapore question.
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Hi!
This is really a proportion question. A full circle is 2π rads and any sector you cut will be a proportion of that as long as you cut from the origin.
So for any sector,
area of sector = (angle in rad) / 2π X area of circle.
Length of arc = (angle in rad) / 2π X circumference.
In this case,
perimeter of shaded region =
24 (base) + 1.855/2π x 2πr (arc)
Area of shaded region =
Area of sector - area of triangle
1.855/2π x πr^2 (area of sector) - 0.5(15)(15)sin1.855rad
I'm using the formula
area of triangle =0.5absin(c)
This is really a proportion question. A full circle is 2π rads and any sector you cut will be a proportion of that as long as you cut from the origin.
So for any sector,
area of sector = (angle in rad) / 2π X area of circle.
Length of arc = (angle in rad) / 2π X circumference.
In this case,
perimeter of shaded region =
24 (base) + 1.855/2π x 2πr (arc)
Area of shaded region =
Area of sector - area of triangle
1.855/2π x πr^2 (area of sector) - 0.5(15)(15)sin1.855rad
I'm using the formula
area of triangle =0.5absin(c)
Date Posted:
3 years ago
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