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:
- Understanding the grid: Each small square in the grid represents a square unit, as indicated by the "1 unit" mark in the image.
- 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:
Do you want more details or have any questions about this process?
Here are some additional questions related to this concept:
- How would the area change if each square was half a unit instead of one unit?
- What is the perimeter of the shaded figure in units?
- How would you calculate the area if the figure was scaled by a factor of 2?
- What is the difference between area and perimeter in this context?
- 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