Problem 63 - Algebra 1: Concepts and Skills

Question

Find the area of the object. The top of a computer desk measures 2 feet by 2 feet.

Step-by-Step Solution

Answer

The area of the top of the computer desk is 4 square feet.

Step 1: Identify the given dimensions

The length and width of the top of the desk are given as: length = 2 feet and width = 2 feet.

Step 2: Apply the Area of a Rectangle formula

The Area of a Rectangle formula is: \(Area = length \times width\). Substituting the given dimensions into this formula, we get: \(Area = 2 feet \times 2 feet\).

Step 3: Compute the area

Multiplying the length and width, we receive that the area of the desk top is \(4 feet^2\).

Key Concepts

Dimensions

Dimensions are the measurements that describe the size of a shape or object. In the case of rectangles, dimensions specifically refer to the length and width of the shape. At a glance, these tell us how long and how wide the rectangle is.
For the computer desk top in our example, both the length and the width are 2 feet. Knowing these two measurements is crucial as they are directly used to calculate the area. Make sure you have clearly identified these measurements before proceeding with any calculations.
The dimensions will always be necessary, whether dealing with small rectangles like a book cover or large ones like a wall.

Formula

A formula is a set of instructions that tells us how to do calculations. For finding the area of a rectangle, we use a simple formula.
The formula to calculate the area of a rectangle is:

• Area = length × width

This means that to find the area, you take the length measurement and multiply it by the width measurement. Remember that this formula works no matter the size of the rectangle, as long as you have the dimensions right.

Rectangle

A rectangle is a four-sided shape with opposite sides that are equal in length and every angle equal to 90 degrees. These properties make rectangles quite easy to work with as every rectangle you encounter will have these consistent characteristics.
Rectangles can vary in size and can be seen in everyday objects like computer screens, doors, and sheets of paper. Understanding what a rectangle is assists in knowing why the formula for the area makes sense—each side's length contributes to the entire surface area, calculated through multiplication.
Always visualize a rectangle as a flat shape on a plane and remember, the longer side is typically called the length and the shorter one the width.

Computation

Computation refers to the mathematical process of calculating or computing something, such as the area. When computing, ensure all values are properly substituted into the formula.
For example, using the area formula for the rectangle:

• Area = length × width
• Substitute: 2 feet × 2 feet = 4 square feet

This computation breaks down into multiplying 2 by 2, which results in an area of 4. It's straightforward and systematic, designed to make the process simple and achievable by following steps carefully.
Computation gives you the final result, and understanding the process builds confidence and clarity when dealing with real-world surfaces.