How to do b?

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# Question

# Answer

(a)

If AB is 26 cm, then half of AB is one diameter = 13 cm, radius = 6.5 cm.

(b)

Those dotted lines are helpful. Each short arc is 1/6 of a circle’s circumference*, so the curved part of the perimeter is 9/6 (= 1.5x) of the circumference (= πd) and the straight part is one diameter (2r, = 13 cm).

Total perimeter = (1.5)(π)(13) + 13 = 74.23 cm.

* Note: from primary school geometric construction (yeah, I still remember how to construct a 60° angle), the intersecting circles make arcs of 60°, so each short arc is 1/6 circle.

(a) Radius of each circle = 26/4 cn = 6.5 cm

(b) Perimeter of the shaded part = 3 * ( perimeter of half circle ) + diameter of a circle

= 3 * ( 1/2 * 2* 3.14 * 6.5 ) + 2 * 6.5

= 74.23 cm

Note : the straight lines in the perimeter is equal to diameter of a circle. The bottom curve parts of the shaeded area perimeter if mirror image to the upper circle would show clearly 3 semicircles diameter.