Math Problem Statement

What is the area of this figure?

Solution

To find the area of this figure, we can break it into smaller sections that are easier to work with, such as rectangles.

Looking at the image, the shape can be divided into two rectangles:

  1. The larger rectangle at the top: It has a length of 8 miles and a height of 7 miles.

    • Area of this rectangle = Length × Height = 8 mi × 7 mi = 56 square miles.
  2. The smaller rectangle at the bottom: It has a length of 5 miles and a height of 3 miles.

    • Area of this rectangle = Length × Height = 5 mi × 3 mi = 15 square miles.

To find the total area of the figure, we need to add the areas of both rectangles:

Total area = 56 square miles + 15 square miles = 71 square miles.

Thus, the area of the figure is 71 square miles.

Would you like more details or have further questions on this?

Here are some related questions:

  1. How do you calculate the area of more complex polygons?
  2. How would you find the area of a figure with curved edges?
  3. Can we apply this method of division to irregular shapes?
  4. What are some real-life applications of calculating area for land plots?
  5. How do different units affect area calculation?

Tip: Breaking complex shapes into smaller, manageable sections simplifies area calculation.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Composite Figures
Rectangles

Formulas

Area of a rectangle = length × width
Area of composite figures = sum of areas of simpler shapes

Theorems

Decomposition of complex shapes into simpler geometric figures

Suitable Grade Level

Grades 5-7