Math Problem Statement

CALCULATE the area of the shape shown in the figure below. The figure consists of a combination of rectangles and a triangle, with sides labeled 4 yards, 6 yards, 6 yards, 3 yards, and 9 yards.

Solution

To calculate the area of the shape, I can divide it into simpler geometric shapes. This figure can be broken down into two rectangles and one triangle.

Here’s how we can approach this:

  1. Bottom Rectangle:

    • Dimensions: 9 yards by 3 yards.
    • Area: Area=9×3=27 square yards\text{Area} = 9 \times 3 = 27 \text{ square yards}.
  2. Top Rectangle:

    • Dimensions: 6 yards by 4 yards.
    • Area: Area=6×4=24 square yards\text{Area} = 6 \times 4 = 24 \text{ square yards}.
  3. Middle Triangle:

    • This is a right triangle.
    • Base: 6 yards, Height: 6 yards.
    • Area: Area=12×6×6=18 square yards\text{Area} = \frac{1}{2} \times 6 \times 6 = 18 \text{ square yards}.

Now, summing up all these areas: Total Area=27+24+18=69 square yards.\text{Total Area} = 27 + 24 + 18 = 69 \text{ square yards}.

So, the area of the shape is 69 square yards.

Do you want more details or have any questions about the process?

Here are some related questions:

  1. How do you find the area of more complex shapes?
  2. How would you calculate the perimeter of this shape?
  3. What happens if the triangle's dimensions change?
  4. How would this shape's area differ if scaled by a factor of 2?
  5. Can the shape be broken down differently to calculate the area?

Tip: When breaking down irregular shapes, try to divide them into familiar geometric figures like rectangles, triangles, or trapezoids.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Composite Shapes

Formulas

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

Theorems

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Suitable Grade Level

Grades 6-8