Question

a circular frame is formed of a wire having circumference 48 cm.this frame is bent to form regular star shape with a number of pointed vertices if angle of each vertex is 60 what will be the length of one edge of the star

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Answer 1

Given :-

• Circumference of circular wire = 48cm.
• This frame id bent to form a regular star shape.
• Angle of each vertex is 60° .

To Find :-

• what will be the length of one edge of the star ?

Solution :-

• when any shape is bent to form a new shape . Than, Perimeter or circumference of both shape remains same.

So,

→ circumference of circular frame = Perimeter of regular star frame = 48cm.

Now,

→ Angle at each vertex = 60° .

Now, as we can see in image ,regular Star with each vertex angle 60° is drawn .

Perimeter of drawn regular star is = Sum of length of all outer edges of regular star = AB + BC + CD + DE + EF + FG + GH + HI + IJ + JK + KL + LA .

since in regular star all edges are equal in length .

Therefore,

→ Perimeter of star = 12 * Length of each edge of star.

→ 48 = 12 * Length of each edge of star

→ Length of each edge of star = (48/12)

→ Length of one edge of star = 4cm. (Ans.)

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