Math Problem Statement

Calculate the area of the given shape by breaking it into rectangles.

Solution

To calculate the area of this shape, we can break it down into two rectangles:

  1. Rectangle A (larger section):

    • Width = 4 cm
    • Height = 7 cm
    • Area of Rectangle A = 4cm×7cm=28cm24 \, \text{cm} \times 7 \, \text{cm} = 28 \, \text{cm}^2
  2. Rectangle B (smaller section on the right):

    • Width = 2 cm
    • Height = 6 cm
    • Area of Rectangle B = 2cm×6cm=12cm22 \, \text{cm} \times 6 \, \text{cm} = 12 \, \text{cm}^2

Total Area of the Shape:
Now, add the areas of the two rectangles: 28cm2+12cm2=40cm228 \, \text{cm}^2 + 12 \, \text{cm}^2 = 40 \, \text{cm}^2

Therefore, the area of the shape is 40 cm².

Would you like more details or have any questions?

Here are some related questions you might find helpful:

  1. How do you calculate the perimeter of a composite shape like this?
  2. How would the area change if one of the dimensions increased by 50%?
  3. Can you solve for the area of other shapes by dividing them into rectangles?
  4. What if this shape was three-dimensional? How would you calculate the volume?
  5. What techniques can be used to find areas of irregular shapes?

Tip: Breaking complex shapes into simpler parts like rectangles or triangles is often the easiest way to calculate their area accurately.

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Math Problem Analysis

Mathematical Concepts

Area calculation
Composite shapes
Rectangles

Formulas

Area of a rectangle: width × height

Theorems

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Suitable Grade Level

Grades 6-8