Math Problem Statement

Find the area of the figure pictured below (two connected rectangles with dimensions 9m, 8m, 4m, and 2m).

Solution

The problem asks to find the area of the irregular figure shown, which consists of two connected rectangles. Let's break it down step by step:

Step 1: Split the figure into two rectangles.

  • Rectangle 1: Dimensions are 9m×4m9 \, \text{m} \times 4 \, \text{m}
  • Rectangle 2: Dimensions are 2m×8m2 \, \text{m} \times 8 \, \text{m}

Step 2: Calculate the area of each rectangle.

  1. Area of Rectangle 1: 9m×4m=36m29 \, \text{m} \times 4 \, \text{m} = 36 \, \text{m}^2
  2. Area of Rectangle 2: 2m×8m=16m22 \, \text{m} \times 8 \, \text{m} = 16 \, \text{m}^2

Step 3: Add the areas of the two rectangles.

Total Area=36m2+16m2=52m2\text{Total Area} = 36 \, \text{m}^2 + 16 \, \text{m}^2 = 52 \, \text{m}^2

Thus, the area of the figure is 52m252 \, \text{m}^2.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

  1. How do you calculate the perimeter of this irregular figure?
  2. How would the area change if one dimension was doubled?
  3. Can you find the area of the figure if it had a triangular section added?
  4. How can you verify if the two rectangles fully cover the entire shape?
  5. How does breaking complex figures into simple shapes help in real-world scenarios?

Tip: Always check if shapes can be divided into simpler ones for easier calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Rectangles

Formulas

Area of a rectangle = length × width

Theorems

Area Addition Postulate

Suitable Grade Level

Grades 6-8