1. **Problem statement:** Calculate the area and perimeter of different types of triangles using the given formulas. 2. **General triangle:** - Area formula: $$P = \frac{1}{2} a h$$ where $a$ is the base and $h$ is the height. - Perimeter formula: $$O = a + b + c$$ where $a$, $b$, and $c$ are the sides. - Heron's formula for area: $$P = \sqrt{s (s - a)(s - b)(s - c)}$$ where $$s = \frac{a + b + c}{2}$$ is the semi-perimeter. 3. **Right triangle:** - Area formula: $$P = \frac{1}{2} a b$$ where $a$ and $b$ are the legs. - Perimeter formula: $$O = a + b + c$$ where $c$ is the hypotenuse. 4. **Isosceles triangle:** - Area formula: $$P = \frac{1}{2} a h$$ where $a$ is the base and $h$ is the height. - Perimeter formula: $$O = a + 2b$$ where $b$ is the length of the equal sides. 5. **Equilateral triangle:** - Area formulas: - $$P = \frac{1}{2} a h$$ - $$P = \frac{h \sqrt{3}}{3}$$ - $$P = \frac{a \sqrt{3}}{2}$$ - $$P = 3a$$ (perimeter) - Height formula: $$h = \frac{a \sqrt{3}}{2}$$ These formulas allow you to calculate the area and perimeter of any triangle type by substituting the known side lengths and heights. **Final note:** Use the appropriate formula depending on the triangle type and known values.