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Fraction of a shape inquiry Mathematical notes For any isosceles triangle Total area

(5b) =

By similar triangles

1

Area unshaded

(2b)

=

Area shaded

–

Fraction shaded

=

1

= (2b)

=

=

For a circle Area of circle

=

Area of semi-circle A =

Area of triangle B Area of triangles B and C θ Area of sector D

Area of sectors D and E Area of shaded segment (A, B, C, D and E) Fraction of circle shaded = 0.62646 (accurate to 5 d.p.), approximately approximately

Fractions of shapes shaded

< square

< circle

triangle