The length and breadth of a painting are 15 cm and 10 cm respectively. A 1 cm wide border is made around the painting. What is the area of the border?
54 sq cm.
Painting Border Area Calculation
We need to find the area of a border surrounding a painting.
Given Dimensions:
- Painting Length ($L_p$) = 15 cm
- Painting Breadth ($B_p$) = 10 cm
- Border Width ($w$) = 1 cm
Step 1: Calculate the Area of the Painting
The area of the painting ($A_p$) is length times breadth.
$A_p = L_p \times B_p$
$A_p = 15 \text{ cm} \times 10 \text{ cm} = 150 \text{ sq cm}$
Step 2: Calculate the Total Dimensions with Border
The border adds 1 cm on each side (top, bottom, left, right). So, the total length and breadth increase by $2 * w$.
- Total Length ($L_{total}$) = $L_p + 2w = 15 \text{ cm} + 2(1 \text{ cm}) = 17 \text{ cm}$
- Total Breadth ($B_{total}$) = $B_p + 2w = 10 \text{ cm} + 2(1 \text{ cm}) = 12 \text{ cm}$
Step 3: Calculate the Total Area
The total area ($A_{total}$) includes the painting and the border.
$A_{total} = L_{total} \times B_{total}$
$A_{total} = 17 \text{ cm} \times 12 \text{ cm} = 204 \text{ sq cm}$
Step 4: Calculate the Area of the Border
The area of the border ($A_{border}$) is the total area minus the painting's area.
$A_{border} = A_{total} - A_p$
$A_{border} = 204 \text{ sq cm} - 150 \text{ sq cm} = 54 \text{ sq cm}$
Conclusion
The area of the border is 54 sq cm.
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