Math Problem Statement

What is the area of the right triangle shown on the grid?

Solution

The image shows a right triangle on a grid where each square represents 1 unit by 1 unit. To find the area of the triangle, we can use the formula for the area of a triangle:

Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

From the grid, we can observe:

  • The base of the triangle is 4 units.
  • The height of the triangle is 3 units.

Substituting these values into the formula:

Area=12×4×3=12×12=6 square units\text{Area} = \frac{1}{2} \times 4 \times 3 = \frac{1}{2} \times 12 = 6 \text{ square units}

The area of the triangle is 6 square units.

Would you like more details or have any questions?

Here are 5 related questions to explore:

  1. How do you calculate the perimeter of this triangle?
  2. Can you find the length of the hypotenuse using the Pythagorean theorem?
  3. How would the area change if the base or height was doubled?
  4. What is the ratio of the triangle's area to the area of the rectangle formed by the base and height?
  5. How can you generalize the area formula for any triangle?

Tip: Remember, the area of any right triangle is half the product of the two sides forming the right angle.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of a Triangle

Formulas

Area of Triangle = (1/2) * base * height

Theorems

Pythagorean Theorem (for potential hypotenuse calculation)

Suitable Grade Level

Grades 6-8