As an architect, you are designing a new house. A window has a height between 140 cm and 150 cm and a width between 74 cm and 70 cm. What are the smallest and largest areas that the window could be?

Verified step by step guidance

1. Step 1: Understand the problem. The area of a rectangle is calculated using the formula: $A=h\times w$, where $h$ is the height and $w$ is the width. We need to find the smallest and largest possible areas given the ranges for height and width.
2. Step 2: Identify the extreme values for height and width. The height ranges from 140 cm to 150 cm, and the width ranges from 70 cm to 74 cm. To find the smallest area, use the smallest height and smallest width. To find the largest area, use the largest height and largest width.
3. Step 3: Calculate the smallest area. Substitute the smallest height (140 cm) and smallest width (70 cm) into the area formula: $A=140\times 70$.
4. Step 4: Calculate the largest area. Substitute the largest height (150 cm) and largest width (74 cm) into the area formula: $A=150\times 74$.
5. Step 5: Conclude that the smallest area corresponds to the smallest height and width, while the largest area corresponds to the largest height and width. These calculations will give you the range of possible areas for the window.

Key Concepts

Area of a Rectangle

The area of a rectangle is calculated by multiplying its height by its width. In this case, the window's dimensions are given in centimeters, and the area will be expressed in square centimeters. Understanding this formula is essential for determining the possible areas of the window based on its varying dimensions.

Measurement Units

Measurement units are crucial in physics and engineering, as they provide a standard for quantifying dimensions. In this scenario, the height and width of the window are given in centimeters, which must be consistently used to calculate the area. Awareness of unit conversions is also important if different units are involved.

Range of Values

The range of values refers to the minimum and maximum limits of a variable. For the window's dimensions, the height ranges from 140 cm to 150 cm, and the width ranges from 70 cm to 74 cm. To find the smallest and largest areas, one must calculate the area using both the minimum and maximum values of height and width.