A courtyard 25 m long and 16 m broad is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is

### Concept & Surface Area Paving To find the total number of items (like bricks or tiles) needed to cover a surface, you divide the total area of the surface by the area of a single item. It is critical that both areas are in the exact same unit of measurement. $$ \text{Number of Bricks} = \frac{\text{Total Area of Courtyard}}{\text{Area of One Brick}} $$ ### Step-by-Step Solution 1. **Find the dimensions of the courtyard in centimeters:** Since the brick dimensions are in cm, it is easiest to convert the courtyard dimensions from meters to centimeters ($1 \text{ m} = 100 \text{ cm}$). $$ \text{Length} = 25 \text{ m} = 25 \times 100 = 2500 \text{ cm} $$ $$ \text{Breadth} = 16 \text{ m} = 16 \times 100 = 1600 \text{ cm} $$ 2. **Calculate the area of the courtyard:** $$ \text{Area of Courtyard} = 2500 \times 1600 = 4,000,000 \text{ cm}^2 $$ 3. **Calculate the area of a single brick:** $$ \text{Area of Brick} = 20 \text{ cm} \times 10 \text{ cm} = 200 \text{ cm}^2 $$ 4. **Calculate the total number of bricks required:** $$ \text{Number of Bricks} = \frac{4,000,000}{200} $$ $$ \text{Number of Bricks} = \frac{40,000}{2} = 20000 $$ ### Exam Strategy & Shortcut To avoid large numbers and multiple zeros which can lead to calculation errors, keep the factors unmultiplied until the final step. Number of bricks $= \frac{2500 \times 1600}{20 \times 10}$. Cancel out the zeros and simplify: $\frac{250 \times 160}{2} = 250 \times 80 = 20000$. ### Common Pitfall The most standard mistake is failing to convert the units. Dividing the courtyard area in $m^2$ ($400$) by the brick area in $cm^2$ ($200$) will give an absurdly small answer of $2$ bricks. Always homogenize units before calculation. ### Final Answer Therefore, the correct answer is **20000**.