1. Let's understand the problem: We need to find the perimeter and area of regular figures, volume and surface area of solids, and area of irregular figures using mathematical methods. 2. For regular figures (like squares, rectangles, triangles, circles), the perimeter is the total length around the figure, and the area is the space inside it. 3. Formulas for some regular figures: - Square: Perimeter $P=4a$, Area $A=a^2$ - Rectangle: Perimeter $P=2(l+w)$, Area $A=lw$ - Triangle: Perimeter $P=a+b+c$, Area $A=\frac{1}{2}bh$ - Circle: Circumference $C=2\pi r$, Area $A=\pi r^2$ 4. For solids, volume is the space inside, surface area is the total area of all surfaces. 5. Formulas for some solids: - Cube: Volume $V=a^3$, Surface Area $SA=6a^2$ - Cylinder: Volume $V=\pi r^2h$, Surface Area $SA=2\pi r(h+r)$ - Sphere: Volume $V=\frac{4}{3}\pi r^3$, Surface Area $SA=4\pi r^2$ 6. For irregular figures, area can be found by dividing the figure into regular shapes, calculating their areas, and summing them. 7. Example: To find the area of an irregular figure, split it into rectangles and triangles, calculate each area using formulas above, then add all areas. This approach uses known formulas and decomposition to find perimeters, areas, volumes, and surface areas as per mathematical methods.