Area Word Problems – Civil Service Exam

Area Word Problems - Civil Service Exam

Overview of Area

The concept of area pertains to the measure of the surface enclosed within the boundary of a two-dimensional shape. It is expressed in square units (such as square meters, square feet, etc.) and is a critical concept in mathematics, especially in geometry, architecture, and real estate, among other fields.

How to Solve for Area

Square

Definition: A square is a four-sided polygon where all sides are equal and each angle is a right angle.
Formula: Area = side length × side length
Example: If a square has a side length of 5 meters, its area is 5 × 5 = 25 square meters.

Rectangle

Definition: A rectangle is a four-sided polygon with opposite sides being equal and each angle being a right angle.
Formula: Area = length × width
Example: For a rectangle with a length of 8 meters and a width of 3 meters, its area is 8 × 3 = 24 square meters.

Triangle

Definition: A triangle is a polygon with three sides and three angles.
Formula: Area = 0.5 × base × height
Example: A triangle with a base of 6 meters and a height of 4 meters has an area of 0.5 × 6 × 4 = 12 square meters. This formula assumes the height is perpendicular to the base.

Circle

Definition: A circle is a round figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
Formula: Area = π × radius²
Example: If a circle has a radius of 7 meters, its area is π × 7² ≈ 153.86 square meters. The constant π (Pi) approximates to 3.14159.

Practice Test on Area Word Problems - Civil Service Exam

Square

Question 1:
Calculate the area of a square with a side length of 7 meters.

Choice A: 49 square meters
Choice B: 35 square meters
Choice C: 28 square meters
Choice D: 14 square meters
Answer: A
Solution:
Area = side length × side length = 7 × 7 = 49 square meters

Question 2:
What is the area of a square whose side measures 12 meters?

Choice A: 144 square meters
Choice B: 130 square meters
Choice C: 120 square meters
Choice D: 156 square meters
Answer: A
Solution:
Area = side length × side length = 12 × 12 = 144 square meters

Rectangle

Question 3:
A rectangular garden measures 15 meters by 8 meters. What is the area of the garden?

Choice A: 100 square meters
Choice B: 110 square meters
Choice C: 120 square meters
Choice D: 130 square meters
Answer: C
Solution:
Area = length × width = 15 × 8 = 120 square meters

Question 4:
Find the area of a rectangle with dimensions 20 meters by 25 meters.

Choice A: 500 square meters
Choice B: 450 square meters
Choice C: 550 square meters
Choice D: 600 square meters
Answer: A
Solution:
Area = length × width = 20 × 25 = 500 square meters

Triangle

Question 5:
A triangle has a base of 10 meters and a height of 6 meters. Calculate its area.

Choice A: 30 square meters
Choice B: 40 square meters
Choice C: 50 square meters
Choice D: 60 square meters
Answer: A
Solution:
Area = 0.5 × base × height = 0.5 × 10 × 6 = 30 square meters

Question 6:
Find the area of a triangle with a base of 14 meters and a height of 8 meters.

Choice A: 56 square meters
Choice B: 66 square meters
Choice C: 76 square meters
Choice D: 86 square meters
Answer: A
Solution:
Area = 0.5 × base × height = 0.5 × 14 × 8 = 56 square meters

Circle

Question 7:
Calculate the area of a circle with a radius of 7 meters.

Choice A: 153.86 square meters
Choice B: 154.00 square meters
Choice C: 150.00 square meters
Choice D: 158.00 square meters
Answer: A
Solution:
Area = π × radius² = π × 7² ≈ 153.86 square meters

Question 8:
A circular pool has a diameter of 14 meters. What is the area?

Choice A: 150.00 square meters
Choice B: 153.86 square meters
Choice C: 154.00 square meters
Choice D: 157.00 square meters
Answer: B
Solution:
Area = π × (radius)² = π × (7)² ≈ 153.86 square meters