The square is one of the simplest yet most frequently tested shapes in Quantitative Aptitude. From perimeter and area to diagonal-based calculations, square questions appear across SSC, Banking, and Railway exams. In this we have provided all the details of square from definitions, formulas, shortcuts, solved questions from recent exams, common mistakes, and smart strategies to solve square-related problems quickly.
Square MCQs Download link
Download Square MCQs highly useful for SSC, Railways by clicking on the link below :
Practice Square Questions (Live)
Below are some geography questions for SSC CGL and other government exam for your practice. Attempt them live and check your score as per the real exam marking scheme. You will get +1 for every correct answer, −0.25 for every wrong answer, and 0 for unattempted questions.
Q.1 A square’s side is increased by 30%. The area increases by:
Q.2 If the diagonal of a square is increased by 40%, its area increases by:
Q.3 The ratio of the area of a square to the area of a square drawn on its diagonal is:
Q.4 A square and an equilateral triangle have equal perimeters. Ratio of their areas is:
Q.5 A square field of area 2 hectares has a path of 2 m wide running inside all around it. Area of the path is:
Q.6 The cost of fencing a square at ₹15/m is ₹2400. What is the cost of tiling it at ₹80/m²?
Q.7 Three squares have sides in ratio 1:2:3. The ratio of their areas is:
Q.8 A square is cut into 4 equal smaller squares. The perimeter of each smaller square compared to the original is:
Q.9 If the perimeter of a square equals the circumference of a circle, and the circle has radius 7 m, the area of the square is:
Q.10 The areas of two squares are in ratio 9:16. The ratio of their diagonals is:
Q.11 A square room’s floor is covered by 400 tiles of 20 cm side. The side of the room is:
Q.12 A man walks along the boundary of a square park at 6 km/h and completes one round in 20 minutes. Area of the park is:
Q.13 The diagonal of a square A is double the side of square B. Ratio of area of A to area of B is:
Q.14 Two squares have sides (x + 4) and (2x − 3). If their perimeters are equal, find x.
Q.15 A square carpet covers 64% of a square room. If the room’s side is 15 m, find the side of the carpet.
Q.16 If each side of a square is increased by ‘a’ metres, the area increases by 88 m². If the original side is 9 m, find ‘a’.
Q.17 A wire of 120 cm is bent first into a square and then into a circle. Ratio of area of square to circle is:
Q.18 A square plot has a 3 m wide road outside on two adjacent sides. If the plot side is 20 m, area of roads is:
Q.19 The side of a square is a rational number. Its diagonal is always:
Q.20 A square of side 8 m and a rectangle of length 16 m have equal areas. What is the perimeter of the rectangle?
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What is Square in Quantitative Aptitude?
A square is a four-sided regular polygon where all sides are equal and all angles are 90°. It is a special case of a rectangle and rhombus.
Why it appears in exams:
Squares are easy to test for geometry basics, mensuration, and number-based applications such as tiling, fencing, and area comparison problems.
Skills required to solve square questions:
- Formula memorization (area, perimeter, diagonal)
- Quick square number calculation
- Ability to relate squares to rectangles and other polygons
Why is Square Important in Competitive Exams?
Square-based problems are among the fastest scoring topics in quantitative aptitude.
| Exam | No. of Questions | Difficulty |
| SSC CGL / CHSL | 1–2 | Easy |
| IBPS PO / SBI PO | 1 | Easy–Moderate |
| RRB NTPC / Group D | 1 | Easy |
| State PSC / Police | 1–2 | Moderate |
Square Quantitative Aptitude Short Notes
Some of the common terms used to solve questions based on squares are as follows:
| Term | Details |
| Side (a) | Length of one side of the square |
| Perimeter | 4 × a |
| Area | a² |
| Diagonal | a√2 |
| Area from diagonal | (Diagonal²) / 2 |
| Perimeter from diagonal | 2√2 × Diagonal |
| Special property | Square is both a rectangle and a rhombus |
| Application | Fencing, tiling, flooring, land measurement |
Formulas Related to Area and Perimeter of Square
The basic formulas used to solve questions based on the area and perimeter of squares are as follows:
| Concept | Details |
| Area | a² |
| Perimeter | 4 × a |
| Diagonal | a√2 |
| Area using diagonal | (d²) / 2 |
| Number of tiles in square area | Area ÷ area of one tile |
| Square in coordinate geometry | Distance formula to verify equal sides |
What are the Types of Square Questions in Quantitative Aptitude?
The types of questions asked on the topic of squares are as follows:
- Direct: Area, perimeter, diagonal from side length
- Application-based: Tiling, fencing, cost calculation
- Mixed-concept: Square combined with rectangles, triangles, or circles
- Puzzle-based: Square arrangements and grid problems
Square Formulas for Quantitative Aptitude
Basic formulas related to the topic of squares are as follows:
| Formula | Details |
| Area = a² | Standard area calculation |
| Perimeter = 4a | Total length around square |
| Diagonal = a√2 | Distance between opposite vertices |
| Area from diagonal = (d²)/2 | When diagonal is known |
| Perimeter from diagonal = 2√2 × d | Reverse calculation |
| Number of tiles = (Area of square) / (Area of one tile) | Tiling problems |
Square Tricks for SSC CGL and Other Exams
The short tricks used to solve questions based on the topic of squares are as follows:
- Memorize the first 30 square numbers for quick calculation.
- Use diagonal formula a√2 to avoid double calculation steps.
- For tiling/fencing problems, convert all units to the same measure before solving.
- In cost problems, multiply cost per unit directly with perimeter or area.
- Eliminate unrealistic options using magnitude comparison before full calculation.
Common Mistakes to avoid while Solving Square Questions
Common mistakes to avoid while solving questions based on the topic of squares are as follows:
- Forgetting to convert units (m ↔ cm).
- Mixing up diagonal and side length formulas.
- Using perimeter formula for area (and vice versa).
- Not squaring correctly for large numbers.
- Skipping diagram for complex application problems.
FAQs
Yes, by verifying equal sides and right angles using distance formula.
Yes, it’s a special type of rhombus with right angles.
Square is a rectangle with all sides equal.
Multiply perimeter or area by rate given.
Divide the diagonal by √2.
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