Math Problem Statement

calculate the area of this shape

calculate the area of this shape

Solution

The shape you've provided can be broken down into simple geometric parts for calculating its area. We can identify several rectangular or trapezoidal sections based on the given measurements.

Here's the breakdown:

  1. Leftmost rectangle: Dimensions: 3 (width) × 4 (height)
  2. Top large rectangle: Dimensions: 16 (width) × 15 (height)
  3. Bottom rectangle: Dimensions: 20 (width) × 4 (height)
  4. Rightmost rectangle (extended section): Dimensions: 7 (width) × 4 (height)

Let's calculate the total area by summing the areas of these parts.The total area of the shape is 360 square units.

Would you like further details or have any questions? Here are a few related questions to consider:

  1. How would the area change if one of the sections was scaled?
  2. Can the shape be divided differently to simplify calculations?
  3. How could you find the perimeter of this shape?
  4. What if this shape represented the floor plan of a building—how would you calculate the materials needed?
  5. Can you calculate the area if part of the shape was a triangle or another irregular polygon?

Tip: Breaking complex shapes into simpler ones is a useful strategy for calculating areas efficiently.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Composite Shapes

Formulas

Area of a rectangle = width × height
Total area = Sum of areas of individual sections

Theorems

Additive Property of Area

Suitable Grade Level

Grades 6-8