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The question is from the topic quadrilaterals. In this problem perimeter and area of a rhombus are given and we have to find out the sum of the lengths of its diagonals. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. It uses the idea of area of rhombus is equal to the sum of the triangles contained in it.

Question 17: Rhombus has a perimeter of 12 and one angle = 120°. Find its area.

  1. 9 * (√3)/2
  2. 3 * (√3)/2
  3. 9 * √3
  4. 18 * √3

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Explanatory Answer

Method of solving this CAT Question from Quadrilaterals: Knowing the properties of rhombus helps.
CAT Question - Geometry - Rhombus

Perimeter = 12.
Let the side of the rhombus be “a?, then 4a = 12 => a = 3.
One angle = 120°.
Adjacent angles of a rhombus are supplementary. Therefore, the other angle = 60°.
Diagonals of a rhombus bisect each other, therefore, ∠DAC = 60° ∠DCA =60° ∠BAC =60°
Therefore, Triangle DAC and BAC are equilateral triangles.
Therefore, Area of Rhombus = 2 * Area of the Equilateral Triangle
= 2 * (√3/4) * a2 = (√3/2) * 9 = 9 * (√3/2).

The question is " Find the area of the rhombus"

Hence, the answer is 9 * (√3/2).

Choice A is the correct answer.


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