Problem 337 - Prealgebra

Question

In the following exercises, solve. NCAA basketball According to NCAA regulations, the dimensions of a rectangular basketball court must be 94 feet by 50 feet. What is the area of the basketball court?

Step-by-Step Solution

Answer

The area of the basketball court is 4700 square feet.

Step 1: Identify the dimensions

Note that the basketball court dimensions are given as 94 feet by 50 feet.

Step 2: Recall the area formula for a rectangle

The formula to find the area of a rectangle is: \[ \text{Area} = \text{Length} \times \text{Width} \]

Step 3: Substitute the dimensions into the formula

Substitute 94 feet for the length and 50 feet for the width into the area formula: \[ \text{Area} = 94 \text{ feet} \times 50 \text{ feet} \]

Step 4: Perform the multiplication

Multiply 94 by 50 to get the area: \[ \text{Area} = 4700 \text{ square feet} \]

Key Concepts

Area Formula

To understand how to calculate the area of a rectangle, you need to know the area formula. The area of any rectangle can be found using a simple equation. The formula is written as:
\[ \text{Area} = \text{Length} \times \text{Width} \]
This formula tells us that to find the area, you multiply the length of the rectangle by its width.
The unit of your result will be square units, like square feet, indicating that the measurement covers a two-dimensional space.

Rectangle Dimensions

Next, let's talk about rectangle dimensions. These are the length and width of the rectangle.
In the case of the NCAA basketball court, the dimensions are given as 94 feet by 50 feet.
Here, the length is 94 feet, which is the longer side of the rectangle, and the width is 50 feet, which is the shorter side.
Knowing the rectangle's dimensions is essential for accurately calculating its area.

Multiplication

Once you have the dimensions and the area formula, the next step is multiplication. This means you will multiply the length by the width.
For our basketball court example, you would do the following:
\[ \text{Area} = 94 \text{ feet} \times 50 \text{ feet} = 4700 \text{ square feet} \]
When performing the multiplication, you multiply the numerical values first (94 times 50 equals 4700).
Then, you combine the units, resulting in square feet (since feet times feet equals square feet).
The final area of the basketball court is 4700 square feet.