Math Problem Statement

What is the area of the rectangle?

What is the area of the rectangle?

Solution

To calculate the area of the shape shown, it appears to be a composite figure rather than a simple rectangle. The figure can be split into basic geometric shapes like rectangles and triangles for easier calculation.

Let's break it down:

  • Step 1: The main section is a rectangle with a width of 14 meters and a height of 18 meters.

    • Area of this rectangle = 14×18=252m214 \times 18 = 252 \, \text{m}^2.
  • Step 2: There is a triangular portion that cuts into the upper-left side of the shape.

    • The base of this triangle is the remaining portion after subtracting 14 meters from the total width of 20 meters. So, base of the triangle = 2014=6meters20 - 14 = 6 \, \text{meters}.
    • The height of the triangle is given as 11 meters.
    • Area of this triangle = 12×base×height=12×6×11=33m2\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 11 = 33 \, \text{m}^2.
  • Step 3: The total area of the composite shape is the area of the rectangle minus the area of the triangular cut-out.

Total area=252m233m2=219m2\text{Total area} = 252 \, \text{m}^2 - 33 \, \text{m}^2 = 219 \, \text{m}^2

Final Answer:

The total area of the shape is 219 square meters (m²).

Would you like a detailed breakdown of the steps, or do you have any other questions? Here are a few related questions to explore:

  1. How do you calculate the perimeter of this composite shape?
  2. What would happen if the triangle was not subtracted but added to the shape?
  3. How can you confirm the dimensions of complex shapes in real-life measurements?
  4. Can you apply the same method to calculate the area of a trapezoidal section?
  5. How does the area formula for a triangle differ from other polygon shapes?

Tip: Always try to break down complex shapes into simpler geometric figures for easier area calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Composite Shapes
Area Calculation

Formulas

Area of a rectangle = length × width
Area of a triangle = ½ × base × height

Theorems

Basic Geometry Area Formulas

Suitable Grade Level

Grades 6-8