Math Problem Statement

What is the total area of the composite shape consisting of two joined rectangles with given dimensions of 12 in × 13 in and 10 in × 10 in?

Solution

The image shows a composite shape that consists of two rectangles joined together. To find the total area of this shape, we need to calculate the area of each rectangle individually and then add them together.

Step-by-step:

  1. Dimensions of the first rectangle (left side):

    • Length = 13 inches
    • Width = 12 inches
    • Area of this rectangle = 13×12=15613 \times 12 = 156 square inches.
  2. Dimensions of the second rectangle (right side):

    • Length = 10 inches
    • Width = 10 inches
    • Area of this rectangle = 10×10=10010 \times 10 = 100 square inches.
  3. Total Area: Total Area=156+100=256square inches\text{Total Area} = 156 + 100 = 256 \, \text{square inches}

So, the total area of the composite shape is 256 square inches.

Do you want further details or have any other questions?


Here are 5 relative questions to expand on this:

  1. What if the dimensions of one rectangle changed, how would that affect the total area?
  2. How do you calculate the perimeter of this composite shape?
  3. Could you split other irregular shapes into simpler shapes for easier area calculation?
  4. What is the formula for finding the area of a triangle, and how does it differ from rectangles?
  5. Can you explain how to find the area of circles or sectors of circles?

Tip: Always break down complex shapes into smaller, familiar shapes (like rectangles, triangles, etc.) for easier calculation!

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of Composite Shapes

Formulas

Area of a rectangle = length × width

Theorems

Area Addition Postulate

Suitable Grade Level

Grades 6-8