FTCE Professional Education Practice Exam

What is the area of a triangle calculated using?

1. 1/3bh

2. bh

3. 1/2bh

4. (a + b + c)/2

The correct answer is: 1/2bh

The area of a triangle is calculated using the formula \( \frac{1}{2}bh \), where \( b \) represents the base of the triangle, and \( h \) is the height measured perpendicular to that base. This formula arises from the fact that a triangle can be thought of as half of a rectangle. If you take a rectangle with length \( b \) and height \( h \), its area is \( bh \). Since a triangle occupies half of that rectangular area, the area of the triangle is therefore expressed as \( \frac{1}{2}bh \). In this context, the other options do not represent the area of a triangle accurately. The term \( \frac{1}{3}bh \) does not apply to triangles, as it does not account for the correct proportional area calculation. The expression \( bh \) would represent the area of a rectangle rather than a triangle, thus misrepresenting the relationship between base and height in triangle geometry. Lastly, the formula \( \frac{(a + b + c)}{2} \) relates to the semi-perimeter of a triangle but does not provide the area.