1. **Stating the problem:** We need to find the area of rectangles using the formula $$A = r \times b$$ where $r$ and $b$ are the lengths of the sides. 2. **Formula and explanation:** The area of a rectangle is calculated by multiplying the length by the breadth. Here, $r$ and $b$ represent these sides. 3. **Calculating areas for each case:** - a) Given side is $6r$, but only one side is given, so area is $6r \times b$ (if $b$ is unknown, area is expressed as $6rb$). - b) Square with side $5r$, so area is $5r \times 5r = 25r^2$. - c) Rectangle with sides $7r$ and $3b$, area is $$7r \times 3b = 21rb$$. - d) Rectangle with sides $9r$ and $4b$, area is $$9r \times 4b = 36rb$$. - e) Rectangle with sides $11r$ and $5b$, area is $$11r \times 5b = 55rb$$. 4. **Finding actual area when $r=3$ cm and $b=4$ cm:** - a) Area = $$6 \times 3 \times 4 = 72$$ cm$^2$ - b) Area = $$25 \times 3^2 = 25 \times 9 = 225$$ cm$^2$ - c) Area = $$21 \times 3 \times 4 = 252$$ cm$^2$ - d) Area = $$36 \times 3 \times 4 = 432$$ cm$^2$ - e) Area = $$55 \times 3 \times 4 = 660$$ cm$^2$ 5. **Volume of solids:** The volume formula is $$Vol = l \times b \times h$$. Since no specific values are given, the volume expressions for solids with dimensions $l$, $b$, and $h$ are simply $$lbh$$. **Summary:** - Areas: a) $6rb$, b) $25r^2$, c) $21rb$, d) $36rb$, e) $55rb$ - Actual areas with $r=3$, $b=4$: a) 72, b) 225, c) 252, d) 432, e) 660 - Volume expressions: $lbh$ for each solid.