Question

In the given figure, AOB & BPC are two semicircles with BCD an equilateral triangle. Find the perimeter of the figure if AB = BC = 14 cm

Answer 1

The perimeter of the figure if AB = BC = 14 cm is 86 cm.

Step-by-step explanation:

In semicircle AOB, we have

AB = 14 cm = diameter of the semicircle

So, the radius of the semicircle, r = d/2 = 14/2 = 7 cm

∴ The circumference of AOB = πr = (22/7) * 7 = 22 cm

Since the length of AB = BC = 14 cm  

Therefore, we can conclude that the circumference of the semicircle BPC is the same as the circumference of AOB i.e., 22 cm.

Now,

In equilateral triangle BCD, we have

BC = CD = DB = 14 cm

∴ The perimeter of the triangle BCD = 3 * side = 3 * 14 = 42 cm

Thus,  

The perimeter of the figure is given by,

= [The circumference of AOB] + [The circumference of the semicircle BPC] + [perimeter of the triangle BCD]

= 22 + 22 + 42

= 86 cm

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Also View:

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