Math Problem Statement

Calculate the area of this L-shaped figure with dimensions as shown.

Solution

To calculate the area of this L-shaped figure, we can break it down into two rectangles:

  1. Rectangle 1 (vertical part):

    • Height = 9 cm
    • Width = 2 cm
    • Area = 9cm×2cm=18cm29 \, \text{cm} \times 2 \, \text{cm} = 18 \, \text{cm}^2
  2. Rectangle 2 (horizontal part):

    • Length = 6 cm
    • Width = 2 cm
    • Area = 6cm×2cm=12cm26 \, \text{cm} \times 2 \, \text{cm} = 12 \, \text{cm}^2

Now, add the areas of these two rectangles to find the total area of the shape:

18cm2+12cm2=30cm218 \, \text{cm}^2 + 12 \, \text{cm}^2 = 30 \, \text{cm}^2

Total Area = 30 cm²

Would you like more details, or do you have any questions?

Here are some related questions to deepen your understanding:

  1. How would you find the perimeter of this shape?
  2. What would the area be if the dimensions were doubled?
  3. How could you calculate the area of other irregular shapes?
  4. How would the area change if the vertical rectangle was only 8 cm tall?
  5. How does breaking shapes down into simpler components help in calculating areas?

Tip: Always look for simple shapes within complex figures to make calculations easier.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Composite Shapes

Formulas

Area = length × width for rectangles

Theorems

Addition of areas of non-overlapping regions

Suitable Grade Level

Grades 5-7