Math Problem Statement

You paint the square sections of the door around the windows. The 3 windows are squares with the side of 7 inches. What is the area of the door you painted?

Solution

To calculate the area of the door you painted, we need to determine the total area of the three windows and then subtract that from the total area of the sections you painted.

Step 1: Calculate the area of one window.

Each window is a square with a side length of 7 inches.

Area of one window=side2=7×7=49 square inches\text{Area of one window} = \text{side}^2 = 7 \times 7 = 49 \text{ square inches}

Step 2: Calculate the total area of all three windows.

There are 3 windows, so:

Total area of the windows=49×3=147 square inches\text{Total area of the windows} = 49 \times 3 = 147 \text{ square inches}

Step 3: Calculate the area of the painted sections.

Assuming the square sections you painted are the exact size as the windows, the area of the door you painted is equal to the total area of the windows, since the painted sections are exactly those squares.

Area of the door painted=147 square inches\text{Area of the door painted} = 147 \text{ square inches}

So, the total area of the door you painted is 147 square inches.

Would you like more details or have any other questions?

Relative Questions:

  1. What is the total area of the door if the dimensions are known?
  2. If the windows had different dimensions, how would the area calculation change?
  3. How would you calculate the area if the door had a different shape or more windows?
  4. What if the sections painted included the area directly around the windows?
  5. How would you calculate the perimeter of the painted sections?

Tip: When dealing with multiple identical shapes, multiply the area of one shape by the number of shapes to quickly find the total area.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Square Geometry

Formulas

Area of a square: side^2

Theorems

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Suitable Grade Level

Grades 5-7