Math Problem Statement

Find the area of the shaded figure.

Solution

To find the area of the shaded figure, let's break down the process:

  1. Understanding the grid: Each small square in the grid represents a square unit, as indicated by the "1 unit" mark in the image.
  2. Counting the shaded squares: The shaded figure appears as a cross shape, composed of individual squares.

Let's count how many full squares are shaded in the cross:

  • The center column consists of 5 shaded squares (3 vertical and 2 horizontal arms of the cross).
  • The horizontal arm consists of 3 shaded squares.

Now let's add them:

  • 3 (horizontal) + 2 + 2 + 1 + 1 (vertical arms and center square) which makes 9 squares.

Thus, the area of the shaded figure is: 9 square units.\boxed{9} \text{ square units}.

Do you want more details or have any questions about this process?

Here are some additional questions related to this concept:

  1. How would the area change if each square was half a unit instead of one unit?
  2. What is the perimeter of the shaded figure in units?
  3. How would you calculate the area if the figure was scaled by a factor of 2?
  4. What is the difference between area and perimeter in this context?
  5. How many vertices does this cross-shaped figure have?

Tip: When working with shapes on a grid, you can often use counting methods for both area and perimeter to simplify your calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Grids

Formulas

Area = sum of shaded unit squares

Theorems

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Suitable Grade Level

Grades 4-6