Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is the formula for the area of a triangle?

1. Area = base * height

2. Area = 1/2 * base * height

3. Area = base + height

4. Area = 2 * base * height

The correct answer is: Area = 1/2 * base * height

The formula for the area of a triangle is derived from the concept of base and height. To calculate the area, you need to determine how much space is enclosed within the triangle's boundaries. In a triangle, the area is calculated as half of the product of its base length and its height. This is expressed in the formula as Area = 1/2 * base * height. The height is the perpendicular line drawn from the apex (the highest point) of the triangle down to the base. Since a triangle can be thought of as being half of a rectangle, where the rectangle's area is found by multiplying the base by the height, it follows that the triangle occupies half of that area, hence the factor of 1/2 in the formula. The other options do not accurately represent the relationship between a triangle's base, height, and area. The choices that simply multiply the base and height or add them do not reflect the actual geometric principles behind the area calculation for triangles.