Math Problem Statement

Find the area of the figure pictured below with dimensions: 4.7 m, 9.9 m, 2.8 m, and 12.3 m.

Solution

To find the area of the given figure, which consists of a combination of rectangular sections, we can break it down into simpler rectangles, calculate the area of each, and then add them up.

Step-by-Step Solution:

  1. Identify Rectangles in the Shape: The figure can be divided into two rectangles:

    • Rectangle 1 (the larger bottom rectangle): It has dimensions 12.3m×9.9m12.3 \, \text{m} \times 9.9 \, \text{m}.
    • Rectangle 2 (the smaller top rectangle): It has dimensions 4.7m×2.8m4.7 \, \text{m} \times 2.8 \, \text{m}.
  2. Calculate the Area of Each Rectangle:

    • Area of Rectangle 1: Area=12.3m×9.9m=121.77m2\text{Area} = 12.3 \, \text{m} \times 9.9 \, \text{m} = 121.77 \, \text{m}^2
    • Area of Rectangle 2: Area=4.7m×2.8m=13.16m2\text{Area} = 4.7 \, \text{m} \times 2.8 \, \text{m} = 13.16 \, \text{m}^2
  3. Add the Areas Together: Total Area=121.77m2+13.16m2=134.93m2\text{Total Area} = 121.77 \, \text{m}^2 + 13.16 \, \text{m}^2 = 134.93 \, \text{m}^2

Final Answer:

The area of the figure is approximately 134.93m2134.93 \, \text{m}^2.

Would you like more details or have any questions?

Here are five related questions for further practice:

  1. How would you find the perimeter of this figure?
  2. What if the shape had an additional rectangle; how would the approach change?
  3. How can you calculate the area if the measurements are in different units (e.g., cm and m)?
  4. How do you find the area of irregularly shaped figures?
  5. How would you calculate the area if the figure included a semicircle on one of its sides?

Tip: When breaking down complex shapes, label each part clearly and solve step-by-step to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Rectangles

Formulas

Area of a rectangle = length × width

Theorems

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Suitable Grade Level

Grades 7-9