Math Problem Statement

What is the area of the triangle shown in the image using the formula: Area of a triangle = base times height divided by 2?

Solution

To find the area of the triangle, we need to use the formula:

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

From the image, we can count the squares to determine the base and height of the triangle.

  • The base of the triangle spans 4 units (4 squares along the grid).
  • The height of the triangle is 4 units (from the top vertex straight down to the base).

Now, applying the values to the formula:

Area=12×4×4=12×16=8\text{Area} = \frac{1}{2} \times 4 \times 4 = \frac{1}{2} \times 16 = 8

Thus, the area of the triangle is 8 square units.

Would you like further details or have any questions?

Here are five related questions you can explore:

  1. How does changing the height affect the area of the triangle?
  2. What happens to the area if both the base and height are doubled?
  3. Can the area formula be applied to triangles that are not right-angled?
  4. How can we find the area if the triangle is on a slanted grid?
  5. How do you find the height if it isn't given directly?

Tip: Always ensure that the base and height are perpendicular when using the area formula for a triangle.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of Triangles
Coordinate Geometry

Formulas

Area of a Triangle = 1/2 * base * height

Theorems

Basic Geometric Theorem for Area Calculation

Suitable Grade Level

Grades 5-7