Question

l m n o p q is a regular hexagon with its side 2 cm , then the area of rectangle m n p q is

Answer 1

Solution :-

We have to find the area of the rectangle MNPQ.

Given - LMNOPQ is a regular hexagon with the each side measuring 2 cm.

MQ, LM and LQ form a 30° +  30° +  120° isosceles triangle with its 2 legs measuring 2 cm each. 

We will use the Law of Sines to find the measurement of MQ. We can drop an altitude from L to divide LMQ into two 30° + 60° + 90° triangle and find MQ/2 from the properties of that triangle. 

LM/Sin(30°) = 2/Sin(30°) = MQ/Sin(120°)

MQ = 2Sin(120°)/Sin(30°) = 2[√(3)/(2)/(1/2)] = 2√(3) 

⇒ [2√(3)](2) 

⇒ 4√3

So, the area of the rectangle MNPQ is 4√3 cm²

Answer.