Math Problem Statement

solve

What is the area of the following figure?

Solution

Let's solve this problem by breaking the figure into two separate parts and finding the area of each:

  1. Breakdown of the Shape:
    • A rectangle on the top left (dimensions: 6m×10m6 \, \text{m} \times 10 \, \text{m}).
    • A right triangle on the bottom right with a base of 4m4 \, \text{m} (10m6m10 \, \text{m} - 6 \, \text{m}) and a height of 5m5 \, \text{m}.

  1. Area of the Rectangle:
    Area of rectangle=length×width=10×6=60m2\text{Area of rectangle} = \text{length} \times \text{width} = 10 \times 6 = 60 \, \text{m}^2

  2. Area of the Triangle:
    The formula for the area of a triangle is:
    Area of triangle=12×base×height\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}
    Substituting the values:
    Area of triangle=12×4×5=10m2\text{Area of triangle} = \frac{1}{2} \times 4 \times 5 = 10 \, \text{m}^2


  1. Total Area:
    Add the areas of the rectangle and triangle:
    Total area=60+10=70m2\text{Total area} = 60 + 10 = 70 \, \text{m}^2

  1. Conclusion:
    The total area of the figure is 70m270 \, \text{m}^2. None of the options provided in the image match this calculation. If you'd like, we can verify or discuss further!

Let me know if you'd like a detailed explanation or corrections.

Here are 5 related questions:

  1. How do you calculate the area of a composite shape with irregular sides?
  2. What is the significance of the base and height in a triangle's area formula?
  3. How can you check your results in an area calculation?
  4. Are there other ways to divide this shape for solving?
  5. Why is it important to ensure dimensions are consistent in calculations?

Tip: When solving composite shapes, always double-check dimensions and breakdown logic!

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Math Problem Analysis

Mathematical Concepts

Area of Composite Shapes
Geometry
Right Triangles

Formulas

Area of a rectangle = length × width
Area of a triangle = 1/2 × base × height

Theorems

Pythagorean Theorem (if necessary for checking triangle dimensions)

Suitable Grade Level

Grades 6-8