Border Area Calculation

This problem requires calculating the area of the border within a rectangular photo frame.

Frame Dimensions

The dimensions of the outer rectangular frame are:

• Width: $30$ cm
• Length: $40$ cm

There is a uniform border of $5$ cm around the photograph.

Photograph Dimensions

The dimensions of the photograph inside the border are found by subtracting twice the border width from the frame dimensions:

• Photograph Length = Frame Length - (2 $\times$ Border Width) = $40 \text{ cm} - (2 \times 5 \text{ cm}) = 40 \text{ cm} - 10 \text{ cm} = 30 \text{ cm}$
• Photograph Width = Frame Width - (2 $\times$ Border Width) = $30 \text{ cm} - (2 \times 5 \text{ cm}) = 30 \text{ cm} - 10 \text{ cm} = 20 \text{ cm}$

Area Calculation

Calculate the area of the outer frame and the inner photograph.

• Area of Frame = Length $\times$ Width = $40 \text{ cm} \times 30 \text{ cm} = 1200 \text{ cm}^2$
• Area of Photograph = Photograph Length $\times$ Photograph Width = $30 \text{ cm} \times 20 \text{ cm} = 600 \text{ cm}^2$

Border Area

Subtract the photograph's area from the frame's area to find the border's area.

Area of Border = Area of Frame - Area of Photograph

Area of Border = $1200 \text{ cm}^2 - 600 \text{ cm}^2 = 600 \text{ cm}^2$