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Chapter 2: Problem 66

Calculate the area of an 8 -by-12-inch picture.

Short Answer

Expert verified
The area of the picture is 96 square inches.

Step by step solution

01

Understand the Problem

We need to find the area of a rectangular picture, which measures 8 inches in height and 12 inches in width.
02

Recall the Formula for Area of a Rectangle

The formula to calculate the area of a rectangle is: \[ \text{Area} = \text{width} \times \text{height} \]
03

Substitute the Values into the Formula

Using the rectangle's dimensions, substitute 12 for the width and 8 for the height into the area formula: \[ \text{Area} = 12 \times 8 \]
04

Calculate the Result

Multiply the two numbers together to find the area: \[ 12 \times 8 = 96 \] So, the area of the picture is 96 square inches.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rectangular Dimensions
When you encounter a problem involving rectangles, the first step is to understand its dimensions. A rectangle is defined by its length (or width) and height (or depth). In our exercise, the rectangle is an 8-by-12-inch picture.

These dimensions are crucial because they directly relate to how we calculate the area. For a rectangle:
  • Width is the longer side, which is 12 inches in this case.
  • Height is the shorter side, which measures 8 inches.
The importance of knowing these dimensions lies in their use in various calculations, such as finding the area, perimeter, or even determining if something will fit in a certain space. It is the foundational step to make any progress in solving related geometric problems.
Calculation of Area
Now, let's explore the process of calculating the area of a rectangle using its dimensions. The area of a rectangle is the amount of space it covers, calculated by multiplying its width by its height.

The formula to find the area is simple:
  • The formula: \( \text{Area} = \text{width} \times \text{height} \)
  • For our example, that's \( 12 \times 8 \).
  • When you multiply these numbers, you get \( 96 \).
This means the rectangle covers 96 square inches. This process is straightforward 鈥� you recall the formula, insert the dimensions, multiply, and you've got your area! Using this method, you can calculate the area of any rectangle whether it's a picture, a room, or a garden.
Educational Mathematics
Understanding these basic math concepts is crucial in educational mathematics. Calculating area is an important skill taught at the foundational level.

It helps students:
  • Understand geometric concepts.
  • Apply math to solve problems in real-world situations.
  • Develop critical thinking and spatial awareness.
In mathematics education, learning to compute the area of rectangles builds the groundwork for more advanced topics, such as volume and surface area calculations of 3-dimensional figures. It also encourages logical reasoning as students must translate a two-dimensional figure into a numerical value representing its space coverage. Remember, practice is key, and these skills enhance your ability to solve a variety of problems, preparing you for future mathematical challenges.

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