Math Problem Statement

What is the area of this figure?

Solution

The figure you uploaded is a compound shape, and the task is to find the area. To do this, we can break the figure into simpler rectangles and find the area of each, then sum the areas.

Step-by-Step Breakdown:

  1. Left Rectangle:

    • Width: 11 mi
    • Height: 4 mi
    • Area = 11×4=44square miles11 \times 4 = 44 \, \text{square miles}
  2. Top Rectangle:

    • Width: 9 mi
    • Height: 3 mi
    • Area = 9×3=27square miles9 \times 3 = 27 \, \text{square miles}
  3. Bottom Right Rectangle:

    • Width: 6 mi (from the height of 11 mi minus the top 3 mi and the small bottom rectangles of 2 mi and 3 mi)
    • Height: 2 mi
    • Area = 6×2=12square miles6 \times 2 = 12 \, \text{square miles}
  4. Small Bottom Rectangle:

    • Width: 3 mi
    • Height: 2 mi
    • Area = 3×2=6square miles3 \times 2 = 6 \, \text{square miles}
  5. Far Right Rectangle:

    • Width: 2 mi
    • Height: 6 mi
    • Area = 2×6=12square miles2 \times 6 = 12 \, \text{square miles}

Total Area:

Adding up all the areas: 44+27+12+6+12=101square miles44 + 27 + 12 + 6 + 12 = 101 \, \text{square miles}

So, the total area of the figure is 101 square miles.

Would you like more details or have any further questions?

Here are 5 related questions:

  1. How would the area change if the top rectangle's width increased by 2 miles?
  2. Can you break down this compound figure in a different way to verify the area?
  3. How does breaking down a complex figure into simpler shapes make calculations easier?
  4. What would the area be if the entire figure were shifted horizontally by 5 miles?
  5. Can you use the same method to find the perimeter of this compound figure?

Tip: Always ensure the dimensions of smaller rectangles add up correctly to match the overall shape!

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of compound figures
Rectangles

Formulas

Area of a rectangle = width × height

Theorems

Additive property of areas

Suitable Grade Level

Grade 6