Math Problem Statement

A rectangular region is removed from another rectangular region to create the shaded region shown below. Find the area of the shaded region.

Solution

The image depicts a shaded region formed by subtracting a smaller rectangle from a larger rectangle. To find the area of the shaded region, we will use the following steps:

Step 1: Calculate the area of the large rectangle.

The dimensions of the large rectangle are 8 feet by 11 feet.

Area of large rectangle=length×width=8×11=88square feet\text{Area of large rectangle} = \text{length} \times \text{width} = 8 \times 11 = 88 \, \text{square feet}

Step 2: Calculate the area of the small rectangle.

The dimensions of the small rectangle are 7 feet by 4 feet.

Area of small rectangle=length×width=7×4=28square feet\text{Area of small rectangle} = \text{length} \times \text{width} = 7 \times 4 = 28 \, \text{square feet}

Step 3: Subtract the area of the small rectangle from the area of the large rectangle to find the shaded region's area.

Area of shaded region=Area of large rectangleArea of small rectangle=8828=60square feet\text{Area of shaded region} = \text{Area of large rectangle} - \text{Area of small rectangle} = 88 - 28 = 60 \, \text{square feet}

Thus, the area of the shaded region is 60 square feet.

Do you need more details or have any questions?

Here are 5 related questions:

  1. What are the steps to calculate the area of irregular shapes?
  2. How do you find the area of a shaded region in a diagram with multiple shapes?
  3. What are some other geometric shapes that can be used to calculate area?
  4. How do you determine the dimensions of a figure when some sides are missing?
  5. How can the concept of area be applied to real-life problems?

Tip: When dealing with areas, always ensure to use the correct units (e.g., square feet, square meters) to avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area calculation
Subtraction of areas

Formulas

Area of a rectangle = length × width
Area of shaded region = Area of large rectangle - Area of small rectangle

Theorems

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Suitable Grade Level

Grades 6-8