Do you remember those geometry classes back in school? The ones where you spent hours drawing circles and triangles, wondering if you’d ever use them? Well, surprise! CAT loves asking questions about these shapes and their properties. 

I remember when I was prepping for my exams, geometry felt like a puzzle I just couldn’t crack. But once I got the hang of it, it became one of my strongest areas.

Let’s break down geometry and mensuration so it doesn’t feel like a nightmare!

The building blocks of Geometry

Understanding geometry is all about shapes, sizes, and properties of space. You will encounter everything you studied in school, from triangles and circles to rectangles and pyramids. It explores the shapes, sizes, positions, and dimensions of objects in both two-dimensional (2D) and three-dimensional (3D) space.

This topic can be your ally if you remember all your formulas and apply some basic brains. If you are just starting to prepare these topics, return to your NCERT Math textbooks and revise your basics. Here’s what to focus on:

• Triangles: Pythagoras theorem, properties of equilateral and isosceles triangles, and concepts like congruence and similarity.
• Circles: Chords, tangents, and sector areas. Trust me, they often appear on the question paper.
• Quadrilaterals: From rectangles to trapezoids, understanding the properties of these four-sided shapes is crucial. Each type has its area formula- make sure you memorise them!
• 3D Shapes: Know your cubes, spheres, and cones. Questions on surface areas and volumes are easy marks for you. 

Mensuration: where formulas shine

Mensuration refers to the branch of geometry that deals with the measurement of geometric shapes and their properties. It is all about precisely applying the correct formula and quick calculation. But never just memorise the formulas; try figuring out how they work.

For instance:

• One must understand that volume is the amount of space an object occupies in three-dimensional space, whereas the surface area measures the total area of the surface of a three-dimensional object.
• Some questions will be straightforward, like finding the volume of a cone, wherein you simply need to apply the formula 1/3πr²h. Other questions can be a bit tricky, like comparing the volume of a cone and a cylinder with the same base and height; you must quickly figure out that the cone’s volume is one-third the volume of the cylinder. So, the ratio of their volumes is 1:3.
• Shortcuts can be a boon when the concept is clear, so try understanding the formulas instead of cramming. If you visualise a cylinder unrolled into rectangles, you will never forget the curved surface area formula, 2πrh.

Patterns come handy

Geometry loves patterns. Whether it’s cyclic quadrilaterals, symmetry in shapes, or repeating sequences in polygons, patterns simplify problems.

I remember tackling a tough problem about a hexagon by breaking it into six equilateral triangles. Suddenly, what looked like a complex problem became super simple- I just needed to calculate the area of one triangle and multiply it by six.

The CAT will not just test your memory but also how well you can break down and simplify problems. So, master your formulas while understanding the logic behind them. Think of every problem as a mini-puzzle waiting to be solved. And for every complex problem you solve, reward yourself with a treat. Take one step (or shape) at a time and keep practising until you have mastered it.