1. Let's start by stating the problem: We want to know the formulas for the area and perimeter of common geometric shapes. 2. For a rectangle: - Area: $A = l \times w$ where $l$ is length and $w$ is width. - Perimeter: $P = 2(l + w)$. 3. For a square (a special rectangle with all sides equal): - Area: $A = s^2$ where $s$ is the side length. - Perimeter: $P = 4s$. 4. For a triangle: - Area: $A = \frac{1}{2} \times base \times height$. - Perimeter: $P = a + b + c$ where $a,b,c$ are the side lengths. 5. For a circle: - Area: $A = \pi r^2$ where $r$ is the radius. - Perimeter (circumference): $C = 2 \pi r$. 6. For a parallelogram: - Area: $A = base \times height$. - Perimeter: $P = 2(a + b)$ where $a$ and $b$ are the lengths of adjacent sides. 7. For a trapezoid: - Area: $A = \frac{1}{2} (b_1 + b_2) \times height$ where $b_1$ and $b_2$ are the lengths of the two parallel sides. - Perimeter: $P = a + b_1 + b_2 + c$ where $a$ and $c$ are the non-parallel sides. These formulas cover the most common shapes for area and perimeter calculations.