AB = BC = CD = DE = 14cm

Each of these lines has length that is ¼ of AE, since AE is made out of these 4 lengths which are equal.

AC = AB + BC = 14 + 14 = 28 cm
Or AC = 2×AB = 2 × 14 = 28 cm

Circumference of circle = 2πr or πd
So circumference of semicircle = πr or ½πd

It is easier to use πr in this question for the big and middle semicircle and ½πd for the small one.

Perimeter = circumference of big semicircle + circumference of medium semicircle + circumference of small semicircle + length DE


= π × AC + π × AB + ½ × π × CD + DE
= 22/7 × 28 + 22/7 × 14 + ½ × 22/7 × 14 + 14
= 88 + 44 + 22 + 14
= 168 cm

Or

22/7 × (AC + AB + ½×CD) + 14
= 22/7 × (28 + 14 + ½ × 14) + 14
= 22/7 × 49 + 14
= 154 + 14
= 168 cm

Alternatively, realise that for these semicircles, the big semicircle has 4 times the diameter and radius of the small one, and the medium semicircle has 2 times the diameter and radius of the small one.

Since the circumference of any semicircle is given by ½πd or πr, then the circumference of the big semicircle is 4 times of the small one.

Likewise, the medium semicircle has a circumference 2 times of the small one.

Circumference of small semicircle
= ½ × π × CD
= ½ × 22/7 × 14
= 22 cm

Perimeter = circumference of small + medium + big semicircle + DE

= 22 + 2 × 22 + 4 × 22 + 14
= 7 × 22 + 14
= 154 + 14
= 168 cm

(22/7)×(2×14+14+7)+14
= 168 cm (Ans)