Math Problem Statement

The image shows a composite shape made of two rectangles. The task is to calculate the total area of the shape based on the given dimensions: 36 in x 36 in for the top rectangle and 72 in x 18 in for the bottom rectangle.

Solution

The image shows a composite shape made of two rectangles, and the goal is to find the area. We can break it down into two simpler parts:

  1. Top Rectangle:

    • Width = 36 inches
    • Height = 36 inches
    • Area of the top rectangle = 36×36=1296square inches36 \times 36 = 1296 \, \text{square inches}
  2. Bottom Rectangle:

    • Width = 72 inches
    • Height = 18 inches
    • Area of the bottom rectangle = 72×18=1296square inches72 \times 18 = 1296 \, \text{square inches}

Now, we add the areas of the two rectangles to get the total area:

Total Area=1296sq in+1296sq in=2592square inches\text{Total Area} = 1296 \, \text{sq in} + 1296 \, \text{sq in} = 2592 \, \text{square inches}

Thus, the total area of the shape is 2592 square inches.

Would you like more details or have any questions?

Here are five related questions:

  1. How do you find the perimeter of this shape?
  2. What would be the area if the top rectangle’s height were doubled?
  3. How would the area change if the bottom rectangle's width were reduced by half?
  4. How can you express the total area in square feet instead of square inches?
  5. Can the shape be divided differently to find the area?

Tip: Breaking complex shapes into smaller rectangles or triangles is a helpful strategy to simplify area calculations.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Composite Shapes

Formulas

Area of a rectangle = width × height

Theorems

Decomposition of composite shapes

Suitable Grade Level

Grades 6-8