Math Problem Statement

What is the area of this figure??

What is the area of this figure?

Solution

To calculate the area of the given figure, we can break it into two rectangles:

Dimensions

  1. The lower rectangle:

    • Width: 9ft9 \, \text{ft}
    • Height: 6ft6 \, \text{ft}
    • Area: 9×6=54ft29 \times 6 = 54 \, \text{ft}^2
  2. The upper rectangle:

    • Width: 4ft4 \, \text{ft}
    • Height: 146=8ft14 - 6 = 8 \, \text{ft} (since 14 ft includes the height of both rectangles)
    • Area: 4×8=32ft24 \times 8 = 32 \, \text{ft}^2

Total Area

Adding the two areas: 54ft2+32ft2=86ft254 \, \text{ft}^2 + 32 \, \text{ft}^2 = 86 \, \text{ft}^2

Thus, the total area of the figure is 86 square feet.

Would you like a detailed breakdown or clarification on any step? Here are five related questions to consider:

  1. How would the calculation change if one dimension were increased or decreased?
  2. What is the perimeter of this figure, given the same dimensions?
  3. How do you determine dimensions of complex shapes from simpler parts?
  4. Could you calculate the area using another method, like dividing it differently?
  5. How would scaling the figure proportionally affect the area?

Tip: When calculating areas of composite shapes, always break them into simpler rectangles, triangles, or other standard shapes for accuracy!

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Math Problem Analysis

Mathematical Concepts

Geometry
Composite Figures
Area Calculation

Formulas

Area of a rectangle = width × height
Area of composite figures = sum of areas of individual shapes

Theorems

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Suitable Grade Level

Grades 5-8