Area perimeter questions hold a significant place in the **quantitative aptitude** sections of competitive exams, playing a crucial role in assessing a candidate’s grasp of geometric concepts and problem-solving abilities.

Here in this blog, students can find 40+ area and perimeter questions, which are part of the quantitative aptitude section of exams.

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## What are Area and Perimeter Questions?

The perimeter of any two-dimensional shape is the length of its boundary whereas the area is the measure of the region enclosed by that shape. The perimeter is basically a length hence measured in units of lengths. Area is length squared hence measured in square units.

**Area Perimeter Formulas**

**Area Circle Formula**

Perimeter | Area | Variables |

2𝜋r | 𝜋r2 | r = radius |

**Area Formula of Square**

Perimeter | Area | Variables |

4a | a2 or d2/2 | a = sided = diagonal |

**Area Formula of Rectangle**

Perimeter | Area | Variables |

2 × (L + B) | L × B | L = length B = breadth |

**Area Formula of Triangle**

Perimeter | Area | Variables |

a + b + c | ½ × Base × Height | a, b, c are lengths of three sides of triangle |

**Area Formula of Equilateral Triangle**

Perimeter | Area | Variables |

3 × a | √3/4 a2 | a = side |

**Area Formula of Isosceles Triangle**

Perimeter | Area | Variables |

2a + b | ¼ b[4a2 – b2]1/2 | a = length of perpendicular sides b = length of unequal side |

**Area Formula of Right Isosceles Triangle**

Perimeter | Area | Variables |

2a + b | a2/2 | a = length of equal sides b = length of unequal side |

**Area Formula of Parallelogram**

Perimeter | Area | Variables |

2(b + h) | b × h | b = base h = height |

**Area Formula of Rhombus**

Perimeter | Area | Variables |

4 × a | ½ (d1 × d2) or base × height | a = sided 1 & d2 are diagonals |

**Area Formula of Trapezium**

Perimeter | Area | Variables |

Sum of all sides | ½ h(a + b) | h = heighta & b are length of parallel sides |

**Area Formula of Kite**

Perimeter | Area | Variables |

2(a + b) | pq/2 | a, b = sides p, q = diagonals |

**Must Read: ****Classification Reasoning Questions | Verbal Reasoning**

## Basic Level Questions on Area and Perimeter

**1. What is the formula for the perimeter (P) of a rectangle with length (l) and width (w)?**

a. P = 2(l + w) b. P = lw c. P = l + w d. P = 2lw

**Answer: a. P = 2(l + w)**

**2. The area (A) of a square is 64 square units. What is the side length of the square?**

a. 6 units b. 8 units c. 4 units d. 10 units

**Answer: b. 8 units**

**3. If the perimeter of a rectangle is 30 units and its length is 10 units, what is the width?**

a. 5 units b. 10 units c. 7.5 units d. 15 units

**Answer: a. 5 units**

**4. What is the formula for the area (A) of a triangle with base (b) and height (h)?**

a. A = 0.5(b + h) b. A = bh c. A = 2bh d. A = (b * h) / 2

**Answer: d. A = (b * h) / 2**

**5. The perimeter of a square is 20 units. What is the length of one side of the square?**

a. 4 units b. 5 units c. 6 units d. 8 units

**Answer: a. 4 units**

**6. If the radius of a circle is 7 units, what is the approximate circumference (C) using π = 3.14?**

a. 21.98 units b. 43.96 units c. 14 units d. 15.7 units

**Answer: b. 43.96 units**

**7. The area of a rectangle is 45 square units, and its length is 9 units. What is the width?**

a. 4 units b. 5 units c. 6 units d. 7 units

**Answer: b. 5 units**

**8. What is the formula for the perimeter (P) of a square with side length (s)?**

a. P = 2s b. P = 4s c. P = s^2 d. P = s/2

**Answer: b. P = 4s**

**9. The circumference (C) of a circle is 31.4 units. What is the approximate radius?**

a. 5 units b. 4 units c. 2 units d. 7 units

**Answer: a. 5 units**

**10. If the diagonal of a square is 10 units, what is the length of each side?**

a. 5 units b. 7 units c. 10 units d. 14 units

**Answer: a. 5 units**

**11. The perimeter of an equilateral triangle is 21 units. What is the length of each side?**

a. 7 units b. 6 units c. 5 units d. 4 units

**Answer: a. 7 units**

**12. The area of a circle is 154 square units. What is the approximate radius?**

a. 7 units b. 14 units c. 5 units d. 4 units

**Answer: a. 7 units**

**13. What is the formula for the perimeter (P) of a regular hexagon with side length (s)?**

a. P = 2s b. P = 3s c. P = 6s d. P = s/2

**Answer: c. P = 6s**

**14. If the area of a rectangle is 30 square units and its length is 6 units, what is the width?**

a. 3 units b. 4 units c. 5 units d. 7 units

**Answer: a. 3 units**

**15. The perimeter of a parallelogram is 18 units, and one side is 5 units. What is the length of the other side?**

a. 6 units b. 8 units c. 10 units d. 12 units

**Answer: b. 8 units**

**16. If the base of a trapezoid is 10 units, the height is 8 units, and the other base is 6 units, what is the area?**

a. 64 square units b. 70 square units c. 52 square units d. 48 square units

**Answer: a. 64 square units**

**17. What is the formula for the area (A) of a rhombus with diagonals (d1 and d2)?**

a. A = 0.5(d1 + d2) b. A = d1 * d2 c. A = (d1 * d2) / 2 d. A = d1 + d2

**Answer: c. A = (d1 * d2) / 2**

**18. The perimeter of a regular octagon is 40 units. What is the length of each side?**

a. 4 units b. 5 units c. 6 units d. 8 units

**Answer: c. 6 units**

**19. If the area of a triangle is 24 square units and its base is 8 units, what is the height?**

a. 4 units b. 3 units c. 6 units d. 5 units

**Answer: b. 3 units**

**20. The circumference of a circle is 36π units. What is the radius?**

a. 6 units b. 9 units c. 12 units d. 18 units

**Answer: a. 6 units**

**21. What is the formula for the perimeter (P) of an isosceles triangle with equal sides (a) and base (b)?**

a. P = 2a + b b. P = a + b c. P = 3a d. P = a + 2b

**Answer: a. P = 2a + b**

**22. The area of a trapezoid is 36 square units, and the height is 4 units. If the bases are in the ratio 3:5, what are the bases?**

a. 6 units and 10 units b. 9 units and 15 units c. 5 units and 8 units d. 12 units and 20 units

**Answer: c. 5 units and 8 units**

**23. If the sides of an equilateral triangle are each 12 units, what is the height of the triangle?**

a. 6√3 units b. 4√3 units c. 3√3 units d. 12 units

**Answer: a. 6√3 units**

**24. The perimeter of a rhombus is 32 units, and one diagonal is 10 units. What is the length of the other diagonal?**

a. 16 units b. 8 units c. 14 units d. 12 units

**Answer: b. 8 units**

**25. If the area of a circle is 154 square units, what is the approximate diameter?**

a. 7 units b. 14 units c. 5 units d. 4 units

**Answer: b. 14 units**

**26. The perimeter of a regular pentagon is 25 units. What is the length of each side?**

a. 4 units b. 5 units c. 3 units d. 6 units

**Answer: b. 5 units**

**27. What is the formula for the area (A) of a sector of a circle with radius (r) and central angle (θ)?** a. A = 0.5rθ b. A = rθ c. A = πr^2 d. A = 2πr

**Answer: b. A = rθ**

**28. The area of a regular hexagon is 54√3 square units. What is the length of each side?**

a. 6 units b. 9 units c. 12 units d. 15 units

**Answer: b. 9 units**

**29. If the perimeter of a rectangle is 24 units and its length is 6 units, what is the width?**

a. 4 units b. 5 units c. 6 units d. 3 units

**Answer: a. 4 units**

**30. The area of a parallelogram is 48 square units, and its base is 8 units. What is the height?**

a. 4 units b. 6 units c. 8 units d. 12 units

**Answer: b. 6 units**

## Advanced Level Questions on Area and Perimeter

- What is the area of a rectangle with length 8 cm and width 5 cm?

a. 30 sq. cm

b. 35 sq. cm

c. 40 sq. cm

d. 45 sq. cm**Answer: c. 40 sq. cm**

- The area of a square is 64 sq. units. What is the length of each side?

a. 6 units

b. 8 units

c. 10 units

d. 12 units**Answer: b. 8 units**

- Calculate the area of a circle with a radius of 6 cm.

a. 18π sq. cm

b. 24π sq. cm

c. 36π sq. cm

d. 48π sq. cm**Answer: c. 36π sq. cm**

- The base of a triangle is 10 cm, and its height is 8 cm. What is the area?

a. 40 sq. cm

b. 48 sq. cm

c. 50 sq. cm

d. 60 sq. cm

Answer: a. 40 sq. cm

- If the area of a parallelogram is 56 sq. units and its base is 8 units, what is its height?

a. 6 units

b. 7 units

c. 8 units

d. 9 units**Answer: a. 6 units**

- Find the area of a trapezoid with bases 5 cm and 8 cm and height 6 cm.

a. 33 sq. cm

b. 42 sq. cm

c. 48 sq. cm

d. 54 sq. cm**Answer: b. 42 sq. cm**

- The area of a rhombus is 96 sq. units, and one diagonal is 12 units. What is the length of the other diagonal?

a. 8 units

b. 10 units

c. 12 units

d. 16 units**Answer: a. 8 units**

- Calculate the area of an equilateral triangle with a side length of 9 cm.

a. 27√3 sq. cm

b. 36√3 sq. cm

c. 45√3 sq. cm

d. 54√3 sq. cm**Answer: b. 36√3 sq. cm**

- The area of a regular hexagon is 108√3 sq. units. What is the length of each side?

a. 3 units

b. 4 units

c. 5 units

d. 6 units**Answer: c. 5 units**

- Find the area of a sector of a circle with a central angle of 60 degrees and a radius of 10 cm.

a. 10π sq. cm

b. 15π sq. cm

c. 20π sq. cm

d. 25π sq. cm**Answer: b. 15π sq. cm**

- The area of a semicircle is 25π sq. units. What is the radius of the circle?

a. 2 units

b. 3 units

c. 4 units

d. 5 units**Answer: b. 3 units**

- A rectangle has a length-to-width ratio of 3:2. If the width is 4 cm, what is the length?

a. 6 cm

b. 8 cm

c. 10 cm

d. 12 cm**Answer: a. 6 cm**

- Calculate the area of a square inscribed in a circle with a radius of 7 cm.

a. 49 sq. cm

b. 64 sq. cm

c. 81 sq. cm

d. 100 sq. cm**Answer: a. 49 sq. cm**

- The area of a pentagon is 120 sq. units. If each side is 8 units, what is the apothem’s length?

a. 7 units

b. 8 units

c. 9 units

d. 10 units**Answer: a. 7 units**

- Find the area of a circular ring with outer radius 10 cm and inner radius 7 cm.

a. 21π sq. cm

b. 28π sq. cm

c. 35π sq. cm

d. 42π sq. cm**Answer: b. 28π sq. cm**

- The area of a quadrilateral is 48 sq. units. If two adjacent sides are perpendicular, what is the length of the shorter side?

a. 6 units

b. 8 units

c. 10 units

d. 12 units**Answer: a. 6 units**

- Calculate the area of an isosceles trapezoid with bases 6 cm and 10 cm and legs of equal length 5 cm.

a. 40 sq. cm

b. 45 sq. cm

c. 50 sq. cm

d. 55 sq. cm**Answer: c. 50 sq. cm**

- The area of a kite is 72 sq. units, and the lengths of its diagonals are 9 units and 16 units. What is the perimeter of the kite?

a. 36 units

b. 42 units

c. 48 units

d. 54 units**Answer: b. 42 units**

- Find the area of a rectangle if its length is tripled and its width is halved.

a. Same as the original area

b. Doubled

c. Tripled

d. Halved**Answer: a. Same as the original area**

- A garden is in the shape of a right-angled triangle with legs 6 m and 8 m. What is the area of the garden?

a. 18 sq. m

b. 24 sq. m

c. 30 sq. m

d. 36 sq. m**Answer: b. 24 sq. m**

- The area of a regular octagon is 160 sq. units. What is the length of each side?

a. 4 units

b. 6 units

c. 8 units

d. 10 units**Answer: b. 6 units**

## Tips to Solve Area and Perimeter Questions

- Familiarize yourself with the formulas for calculating the area of different shapes. Regularly practice applying these formulas to solve problems.
- For composite shapes, break down the problem into simpler components. Calculate the area of each component and sum them up.
- Develop the ability to visualize geometric shapes, especially in real-world scenarios. This visualization will aid in selecting the appropriate formula.
- If aiming for competitive exams with advanced geometry concepts, delve into more complex applications of area, such as irregular shapes or using theorems from geometry.

**Also Read: ****Questions of Syllogism Reasoning | Verbal Reasoning**

## FAQs

Why are area questions important in competitive exams?

Area questions assess geometric understanding, a foundational concept in quantitative aptitude. Mastery is vital for various competitive exams.

How can I efficiently solve area questions with complex shapes?

Break down complex shapes into simpler ones, apply the relevant formulas to each component, and sum the areas for an efficient solution.

Are real-world applications of area important for competitive exams?

Yes, understanding how to apply area concepts to real-world scenarios enhances problem-solving skills and is frequently tested in competitive exams.

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