Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

What is the formula for the area of a triangle?

1. A = (1/2)bh

2. P = side + side + side

3. V = lwh

4. SA = 2(wl + hl + hw)

The correct answer is: A = (1/2)bh

The formula for the area of a triangle is given by \( A = \frac{1}{2}bh \), where \( b \) represents the base of the triangle and \( h \) represents the height. This formula is derived from the concept that a triangle can be thought of as half of a rectangle. To visualize this, if you take a rectangle and draw a diagonal from one corner to the opposite corner, you divide the rectangle into two equal triangles. The area of the rectangle can be calculated using the formula \( A = bh \), where the base is the length of one side and the height is the perpendicular distance from the base to the opposite side. Since a triangle occupies half the space of the rectangle, the area of the triangle is therefore half of the rectangle's area, which leads to the formula \( A = \frac{1}{2}bh \). The other formulas presented in the choices pertain to different geometric calculations: perimeter, volume of a rectangular prism, and surface area of a rectangular box, respectively, which do not apply to the calculation of a triangle's area.