Problem 333 - Prealgebra

Question

In the following exercises, solve. Painting Jane is painting one wall of her living room. The wall is rectangular, 13 feet wide by 9 feet high. What is the area of the wall?

Step-by-Step Solution

Answer

The area of the wall is 117 square feet.

Step 1 - Identify the dimensions

The problem states that the wall is 13 feet wide and 9 feet high. These are the dimensions we will use to find the area.

Step 2 - Use the area formula

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

Step 3 - Substitute the values

Substitute the given dimensions into the formula: \[ \text{Area} = 13 \text{ ft} \times 9 \text{ ft} \]

Step 4 - Calculate the area

Perform the multiplication: \[ 13 \times 9 = 117 \text{ square feet} \]

Step 5 - State the final answer

The area of the wall is 117 square feet.

Key Concepts

Finding Area

Understanding how to calculate the area is a fundamental concept in geometry. The area is the amount of space inside a two-dimensional shape. For rectangles, the area can be calculated using a simple formula. In this problem, you are asked to find the area of a rectangular wall. We use the dimensions provided (13 feet wide and 9 feet high) to find the total area. By multiplying the width by the height, you can determine how much space is inside the rectangle. This gives us the formula: \[ \text{Area} = \text{width} \times \text{height} \] Applying the given dimensions: \[ \text{Area} = 13 \text{ ft} \times 9 \text{ ft} = 117 \text{ square feet} \] Hence, the area of the wall is 117 square feet.

Geometry Basics

Geometry is a branch of mathematics that deals with shapes, sizes, and the properties of space. One basic concept is the calculation of the area of different shapes, such as rectangles, squares, and triangles. A rectangle has four sides, with opposite sides being equal in length. To solve problems involving the area of a rectangle, you need to know its width and height. These dimensions are multiplied together. Understanding these basic principles helps in solving various real-life problems, like determining how much paint is needed to cover a wall.

Multiplication

Multiplication is one of the basic arithmetic operations and is essential for calculating areas. When you multiply two numbers, you are essentially adding a number to itself a certain number of times. For example, in our problem, multiplying 13 by 9 is like adding 13 repeatedly, 9 times: \[ 13 + 13 + 13 + 13 + 13 + 13 + 13 + 13 + 13 \] Using the multiplication formula: \[ 13 \times 9 = 117 \] Mastering multiplication makes it easier to solve problems quickly and efficiently. For areas, you use multiplication to combine the dimensions of a shape and find the total space inside.