Math Problem Statement

What is the area?

Solution

To calculate the area of the given shape, let's break it into simpler rectangles, compute their individual areas, and then sum them.

Observations from the image:

  1. The shape appears to be an L-shaped figure that can be divided into two rectangles:
    • Top rectangle with dimensions 6cm×4cm6 \, \text{cm} \times 4 \, \text{cm}.
    • Bottom rectangle with dimensions 2cm×3cm2 \, \text{cm} \times 3 \, \text{cm}.

Step-by-Step Calculation:

1. Area of the top rectangle:

Areatop=Length×Width=6cm×4cm=24cm2\text{Area}_{\text{top}} = \text{Length} \times \text{Width} = 6 \, \text{cm} \times 4 \, \text{cm} = 24 \, \text{cm}^2

2. Area of the bottom rectangle:

Areabottom=Length×Width=2cm×3cm=6cm2\text{Area}_{\text{bottom}} = \text{Length} \times \text{Width} = 2 \, \text{cm} \times 3 \, \text{cm} = 6 \, \text{cm}^2

3. Total Area:

Total Area=Areatop+Areabottom=24cm2+6cm2=30cm2\text{Total Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{bottom}} = 24 \, \text{cm}^2 + 6 \, \text{cm}^2 = 30 \, \text{cm}^2

Final Answer:

The area of the shape is: 30cm2\boxed{30 \, \text{cm}^2}

Would you like further clarifications or have additional questions?


Related Questions:

  1. How would the area change if the dimensions of the top rectangle doubled?
  2. Can this shape be divided into more complex sub-regions for other calculations?
  3. How would you calculate the perimeter of this L-shaped figure?
  4. What real-world applications involve calculating the areas of irregular shapes?
  5. How can we generalize the process of finding areas for more complicated composite shapes?

Tip:

When dealing with composite shapes, always break them into simpler shapes, calculate their areas individually, and then sum them.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Composite Shapes

Formulas

Area of a rectangle = length × width

Theorems

Decomposition of composite shapes into rectangles

Suitable Grade Level

Grades 4-6