CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

The question is from the topic quadrilaterals. In this problem side and angle of a rhombus are given and we have to find out the area of the rhombus. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. Triangles are heavily tested, the wonderful infinite-sided polygon that is the circle is also heavily tested. In between these two lies this great mass of regular polygons.

Question 21: Rhombus of side 6 cm has an angle equal to the external angle of a regular octagon. Find the area of the rhombus.

1. 18√2 cm²
2. 9√2 cm²
3. 15√2 cm²
4. 12√2 cm²

Explanatory Answer

Method of solving this CAT Question from Quadrilaterals: Basic knowledge about regular polygon helps.

Side of the rhombus 's' = 6 cm
Angle between sides 'a' = exterior angle of an octagon
Therefore a = 45 degrees
Area of rhombus = sin a * s²
Area = (1/√2) * 36
Area = 18√2 cm²

The question is "Find the area of the rhombus."

Hence, the answer is 18√2 cm².

Choice A is the correct answer.