Math Problem Statement

Find the area of the shaded figure (a square) in a grid where each square unit represents 1 unit by 1 unit.

Solution

To find the area of the shaded figure, we will calculate the area of the square based on the grid and unit measurement.

Step-by-step solution:

  1. Each square in the grid represents 1 unit by 1 unit.
  2. The shaded square occupies a grid of 4 units by 4 units.
  3. The area AA of a square is calculated by the formula: A=side length2A = \text{side length}^2
  4. Since the side length is 4 units: A=42=16 square unitsA = 4^2 = 16 \text{ square units}

Final Answer:

The area of the shaded figure is 16 square units.

Would you like further details or clarifications? Here are five related questions that expand on this:

  1. What is the formula for finding the area of a rectangle or other quadrilaterals?
  2. How does the area change if the side length of the square is doubled?
  3. How can you find the perimeter of the shaded figure?
  4. How would the area calculation change for other polygon shapes?
  5. What are some real-world applications of calculating area for squares?

Tip: When dealing with grids, counting the squares or using unit measurements is an efficient way to calculate areas of regular shapes.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Squares

Formulas

Area of a square = side length^2

Theorems

Properties of squares
Area of two-dimensional shapes

Suitable Grade Level

Grades 4-6