In-Depth: 2D Geometry (Area/Perimeter)

CLAT Application & Relevance

Importance: Medium. Mensuration in CLAT is almost always applied within a Data Interpretation context, often as part of a caselet. You won't typically solve pure geometry theorems. Instead, you'll need to calculate areas, perimeters, or dimensions of basic 2D shapes (rectangles, squares, circles, triangles) when numerical information is given in a passage, for problems related to land, construction, layout, or costing.

How it's tested: Calculating the cost of fencing a rectangular plot; finding the area of a circular track; comparing the perimeters of different shaped regions given their dimensions; problems involving paths inside/outside shapes.

Section 1: Core Concepts & Formulas

2D (two-dimensional) geometry deals with flat shapes that have only length and width. Key concepts include Perimeter (the boundary length) and Area (the surface enclosed by the boundary).

Key Formulas for Common 2D Shapes

Square:
- Side = 'a'
- Perimeter = 4a
- Area = a²
- Diagonal = a√2
Rectangle:
- Length = 'l', Width = 'w'
- Perimeter = 2(l + w)
- Area = l × w
- Diagonal = √(l² + w²)
Circle:
- Radius = 'r', Diameter = 'd' (where d = 2r)
- Circumference (Perimeter) = 2πr or πd
- Area = πr²
- Value of π (Pi) ≈ 22/7 or 3.14
Triangle:
- Base = 'b', Height = 'h'
- Area = (1/2) × b × h
- For Right-angled Triangle: Area = (1/2) × Product of sides forming the right angle
- For Equilateral Triangle (side 'a'): Area = (√3 / 4) × a²
- Perimeter = Sum of all three sides.
Parallelogram: Area = Base × Height
Trapezium: Area = (1/2) × (Sum of parallel sides) × Height

Section 2: Solved CLAT-Style Examples

Example 1: Area and Cost Calculation for a Rectangular Plot (Caselet)

Passage Context: "A city's urban development department, following a new legal policy, decided to convert a rectangular plot of land into a public park. The length of the plot is 40 meters, and its width is 25 meters. The department plans to cover the entire park with special eco-friendly grass, which costs ₹150 per square meter. A pathway of 2 meters width is to be built along the boundary (inside) of the park for walking."

Question A: "What is the total cost of covering the park with grass?"

Question B: "What is the area of the pathway?"

Detailed Solution A (Total Cost of Grass):
1. Calculate Area of the Park: Area = Length × Width = 40 m × 25 m = 1000 square meters.
2. Calculate Total Cost of Grass: Total Cost = Area × Cost per sq meter = 1000 sq m × ₹150/sq m = ₹1,50,000.
Answer A: The total cost of covering the park with grass is ₹1,50,000.

Detailed Solution B (Area of Pathway):
1. Dimensions of Inner Area (after pathway): Length of inner area = Original Length - 2 × Pathway Width = 40 - 2 × 2 = 40 - 4 = 36 m. Width of inner area = Original Width - 2 × Pathway Width = 25 - 2 × 2 = 25 - 4 = 21 m.
2. Calculate Area of Inner Area: Area_inner = 36 m × 21 m = 756 square meters.
3. Calculate Area of Pathway: Area_Pathway = Area of Park (Total) - Area of Inner Area = 1000 sq m - 756 sq m = 244 square meters.
Answer B: The area of the pathway is 244 square meters.

Example 2: Circle's Circumference and Area in a Problem

Passage Context: "A lawyer has a round table in their office with a diameter of 1.4 meters. They wish to place a protective cover that hangs 10 cm over the edge around the entire table."

Question A: "What is the area of the table surface that needs to be covered?" (Use π = 22/7)

Question B: "What is the length of the decorative lace required for the edge of the cover (including the overhang)?"

Detailed Solution A (Area of Table Surface):
1. Find Radius: Diameter = 1.4 m. Radius (r) = 1.4 / 2 = 0.7 m.
2. Apply Area of Circle Formula: Area = πr²
= (22/7) * (0.7)²
= (22/7) * 0.49
= 22 * 0.07 = 1.54 square meters.
Answer A: The area of the table surface to be covered is 1.54 square meters.

Detailed Solution B (Length of Lace for Cover Edge):
1. Convert Overhang to Meters: 10 cm = 0.1 m.
2. Calculate New Radius of the Cover (including overhang): New Radius = Table Radius + Overhang = 0.7 m + 0.1 m = 0.8 m.
3. Apply Circumference Formula for New Radius: Circumference = 2πr
= 2 * (22/7) * 0.8
= (44/7) * 0.8 ≈ 6.2857 * 0.8 ≈ 5.028 meters.
Answer B: Approximately 5.03 meters of decorative lace is required.