TANCET 2008 - Old test paper solution : Area of rectangle in a regular hexagon, mensuration, geometry : Ascent Education TANCET MBA Classes

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You are here: Home   TANCET Prep Questions  Mensuration, Solid Geometry   TANCET 2008 Question 19

TANCET 2008 Quant - Regular Hexagon Area

Mensuration Question 16

The hexagon ABCDEF is regular. That means all its sides are of the same length and all its interior angles are of the same size. Each side of the hexagon is 2m. What is the area of the rectangle BCEF?
Regular hexagon of side 2m
  1. 4 sq.m
  2. 4 root 3 sq.m
  3. 8 sq.m
  4. 4 + 4 root 3 sq.m
  5. 12 sq.m
Correct Answer : 4 root 3 sq.m. Choice (2)

Explanatory Answer

regular hexagon showing 6 equilateral triangles
A regular hexagon comprises six equilateral triangles - each of side 2 m, the measure of the side of the regular hexagon - as shown above. The 6 triangles are numbered 1 to 6 in the figure shown above.

BX is the altitude of triangle 1 and XF is the altitude of triangle 2.
Both triangle 1 and triangle 2 are equilateral triangles.

regular hexagon showing 6 equilateral triangles
Hence, BX = XF = root 3/2 * 2
Therefore, BF, the length of the rectangle = 2 root 3 m

Hence, the area of the rectangle BCEF = length * width = 2 root 3*2 = 4 root 3 sq.m

Level of difficulty : Moderate

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