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Question

A 60 angle is constructed with arc radius as 4 cm. Find the area of the BOC.


A
43 cm2
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B
3 cm2
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C
12 cm2
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D
16 cm2
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Solution

The correct option is A 43 cm2
Steps of construction of 60 angle:
Step 1 : Draw the given ray OA and taking O as centre and radius = 4 cm, draw an arc which intersects OA, say at a point B.
Step 2 : Taking B as centre and with the same radius, draw an arc intersecting the previously drawn arc at a point C.
Step 3 : Draw a ray OD Passing through C then BOC is the required angle of 60°.

In OBC
OB = OC [radii of same arc]
OB = BC [Arcs of equal radius]
Then OB = OC = BC = 4 cm. [Same arc with same radii]
OBC is equilateral triangle.

Area of an equilteral triangle
= 34×side2=34×42

= 43 cm2

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