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Question

ABCD is a rectangle such that CAB=60° and AC = a units. The area of rectangle ABCD is  _______.
  1. 23a2 sq. units
  2. 32a2 sq. units
  3. 34a2 sq. units
  4. 38a2 sq. units


Solution

The correct option is C 34a2 sq. units
 

In ABC, right angled at B
sin 60°=BCAC
32=BCaBC=32a

cos 60°=ABAC
12=ABaAB=a2

So, area of the rectangle 
=AB×BC=a2×32a=3a24

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