Math Problem Statement

answer the question please

What is the area of this figure?

Solution

To find the area of this composite figure, we can break it down into simpler rectangles, calculate the area of each rectangle, and then sum them up.

The figure consists of multiple rectangles that can be identified as follows:

1. Left horizontal rectangle:

  • Dimensions: 12 cm by 3 cm
  • Area = 12×3=36cm212 \times 3 = 36 \, \text{cm}^2

2. Top rectangle:

  • Dimensions: 9 cm by 6 cm
  • Area = 9×6=54cm29 \times 6 = 54 \, \text{cm}^2

3. Middle-right rectangle:

  • Dimensions: 6 cm by 4 cm
  • Area = 6×4=24cm26 \times 4 = 24 \, \text{cm}^2

4. Bottom-right rectangle:

  • Dimensions: 9 cm by 7 cm
  • Area = 9×7=63cm29 \times 7 = 63 \, \text{cm}^2

5. Small rectangle in the middle:

  • Dimensions: 8 cm by 6 cm
  • Area = 8×6=48cm28 \times 6 = 48 \, \text{cm}^2

Now, let's add the areas of these individual rectangles to find the total area:

36+54+24+63+48=225cm236 + 54 + 24 + 63 + 48 = 225 \, \text{cm}^2

Thus, the total area of the figure is 225 square centimeters.

Would you like further details on any specific part of the calculation?

Related Questions:

  1. How do you calculate the area of a composite figure with curved sections?
  2. What is the formula for finding the area of a triangle?
  3. Can the same method be used to find the perimeter of this figure?
  4. How would you find the volume of a 3D shape based on this figure as a base?
  5. What are other methods to calculate areas of complex figures?

Tip: When dealing with complex figures, always try to divide them into basic geometric shapes like rectangles, triangles, or circles for simpler calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Composite Figures
Area Calculation

Formulas

Area of a rectangle = length × width

Theorems

None specific, uses basic area calculation

Suitable Grade Level

Grades 5-7