Math Problem Statement

find shaded area

Find shaded area

Solution

To calculate the shaded area of the figure:

  1. Shape Analysis: The shaded region appears to be a right triangle formed by dividing a square into two halves diagonally.

  2. Square Dimensions: Count the total grid squares along one side of the square. The grid is 6×66 \times 6, so the side length of the square is 6 units.

  3. Area of the Square:
    Area of Square=side2=62=36units2\text{Area of Square} = \text{side}^2 = 6^2 = 36 \, \text{units}^2

  4. Area of the Triangle: The triangle is half of the square:
    Area of Triangle=Area of Square2=362=18units2\text{Area of Triangle} = \frac{\text{Area of Square}}{2} = \frac{36}{2} = 18 \, \text{units}^2

Thus, the shaded area is 18 square units.

Would you like further clarification or help with related concepts?

Related Questions:

  1. How do you find the area of a triangle generally?
  2. What is the formula for the area of a square and how does it apply here?
  3. How does dividing shapes diagonally affect their area?
  4. How would this calculation change if the square were not perfectly divided?
  5. What are some real-world applications of this type of calculation?

Tip:

Always verify the dimensions or counting in grids to avoid minor miscalculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Triangles
Squares

Formulas

Area of a square = side^2
Area of a triangle = (1/2) * base * height

Theorems

Area division of a square by its diagonal results in two equal triangles

Suitable Grade Level

Grades 6-8