Perimeter Problems – Civil Service Exam

Perimeter Problems - Civil Service Exam

Overview of Perimeter

The perimeter is a fundamental geometric concept that represents the total length around the boundary of a two-dimensional shape. It is typically measured by summing the lengths of all the sides of the shape. The computation of the perimeter varies depending on the geometry of the shape in question. Here’s a quick overview of how to compute the perimeter for common shapes such as squares, rectangles, triangles, and circles.

Square

Definition: A square is a four-sided polygon where all sides are equal in length and each angle is a right angle.
Formula: Perimeter = 4 × side length
Example: If one side of a square is 5 meters, its perimeter is 4 × 5 = 20 meters.

Rectangle

Definition: A rectangle is a four-sided polygon with opposite sides equal in length and each angle is a right angle.
Formula: Perimeter = 2 × (length + width)
Example: If a rectangle has a length of 10 meters and a width of 7 meters, its perimeter is 2 × (10 + 7) = 34 meters.

Triangle

Definition: A triangle is a polygon with three sides and three angles.
Formula: Perimeter = side₁ + side₂ + side₃
Example: For a triangle with sides of 3 meters, 4 meters, and 5 meters, its perimeter is 3 + 4 + 5 = 12 meters.

Circle

Definition: A circle is a round shape with all points at the boundary equidistant from the center.
Formula for Perimeter (Circumference): Perimeter = 2π × radius or π × diameter
Example: If a circle has a radius of 3 meters, its perimeter is 2 × 3.14159 × 3 ≈ 18.85 meters.

Practice Test on Perimeter Problems - Civil Service Exam

Square

Question 1:
A square garden has a side length of 4 meters. What is the perimeter of the garden?

Choice A: 16 meters
Choice B: 12 meters
Choice C: 8 meters
Choice D: 14 meters
Answer: A
Solution:
Perimeter of a square = 4 × side length
Perimeter = 4 × 4 = 16 meters

Question 2:
Each side of a square playground measures 9 meters. What is the perimeter of the playground?

Choice A: 36 meters
Choice B: 18 meters
Choice C: 27 meters
Choice D: 45 meters
Answer: A
Solution:
Perimeter of a square = 4 × side length
Perimeter = 4 × 9 = 36 meters

Rectangle

Question 3:
A rectangular room measures 8 meters in length and 6 meters in width. What is the perimeter of the room?

Choice A: 28 meters
Choice B: 26 meters
Choice C: 24 meters
Choice D: 30 meters
Answer: A
Solution:
Perimeter of a rectangle = 2 × (length + width)
Perimeter = 2 × (8 + 6) = 28 meters

Question 4:
The length of a rectangular park is 15 meters and the width is 10 meters. Calculate the perimeter of the park.

Choice A: 40 meters
Choice B: 50 meters
Choice C: 60 meters
Choice D: 70 meters
Answer: B
Solution:
Perimeter of a rectangle = 2 × (length + width)
Perimeter = 2 × (15 + 10) = 50 meters

Triangle

Question 5:
A triangle has sides of lengths 5 meters, 7 meters, and 10 meters. What is the perimeter of the triangle?

Choice A: 20 meters
Choice B: 22 meters
Choice C: 18 meters
Choice D: 24 meters
Answer: B
Solution:
Perimeter of a triangle = sum of all sides
Perimeter = 5 + 7 + 10 = 22 meters

Question 6:
Find the perimeter of a triangle with sides measuring 4 meters, 6 meters, and 9 meters.

Choice A: 15 meters
Choice B: 19 meters
Choice C: 20 meters
Choice D: 17 meters
Answer: B
Solution:
Perimeter of a triangle = sum of all sides
Perimeter = 4 + 6 + 9 = 19 meters

Circle

Question 7:
A circular fountain has a radius of 3 meters. What is the perimeter (circumference) of the fountain?

Choice A: 18.85 meters
Choice B: 19.42 meters
Choice C: 20.11 meters
Choice D: 17.28 meters
Answer: A
Solution:
Perimeter (Circumference) of a circle = $2 π \times radius$
Perimeter = ≈ 18.85 meters

Question 8:
Find the perimeter (circumference) of a circular garden with a diameter of 10 meters.

Choice A: 31.42 meters
Choice B: 32.56 meters
Choice C: 28.27 meters
Choice D: 35.34 meters
Answer: A
Solution:
Perimeter (Circumference) of a circle =
Perimeter = ≈ 31.42 meters