What is the formula for the area of a triangle?

• A. Base + Height
• B. 1/2 Base x Height
• C. Base x Height
• D. Height squared

Answer: (B)

The correct formula for the area of a triangle is derived from the fundamental principles of geometry. The area measures the space within the triangle's boundaries and can be calculated by taking half of the product of the base and height.

The concept is built on the understanding that a triangle can be thought of as half of a rectangle. The area of a rectangle is calculated by multiplying its length (base) by its width (height). Since a triangle has one of its angles pointing up or down, it occupies half the area of a rectangle that has the same base and height. Therefore, to find the area of a triangle, you multiply the base by the height and then take half of that product, resulting in the formula:

Area = 1/2 × (Base × Height).

This method of calculation allows for an accurate representation of the area that is consistent with the geometric properties of triangles.