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.