Question

problems 2 - 4: determine the area of each triangle in square centimeters.

Explanation:

Step1: Recall triangle - area formula

The formula for the area of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Solve for problem 2

For the right - triangle in problem 2 with base $b = 12$ cm and height $h = 5$ cm, we substitute into the formula: $A=\frac{1}{2}\times12\times5$.
$A = 30$ $cm^{2}$.

Step3: Solve for problem 3

For the triangle in problem 3 with base $b = 12$ cm and height $h = 8$ cm, we substitute into the formula: $A=\frac{1}{2}\times12\times8$.
$A=48$ $cm^{2}$.

Step4: Solve for problem 4

For the right - triangle in problem 4 with base $b = 6$ cm and height $h = 5$ cm, we substitute into the formula: $A=\frac{1}{2}\times6\times5$.
$A = 15$ $cm^{2}$.

Answer:

Problem 2: 30 $cm^{2}$
Problem 3: 48 $cm^{2}$
Problem 4: 15 $cm^{2}$