A rectangular photo frame of size 30 cm $\times$ 40 cm has a photograph mounted at the centre leaving a 5 cm border all around. The area of the border is
$600 \text{ cm}^2$
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 = $1200 \text{ cm}^2 - 600 \text{ cm}^2 = 600 \text{ cm}^2$
Important Questions from Mensuration 2D (Notes)
- $P_1$ and $P_2$ are two regular polygons. The sum of all the interior angles of $P_1$ is $1800^\circ$. Each interior angle of $P_2$ exceeds its exterior angle by $120^\circ$. The difference between the number of sides of $P_1$ and $P_2$ is:
- The perimeter of the triangle is 24 cm and if the sides of the triangles are by prime numbers then the half of the area of triangle (in $cm^2$) is:
- The area of a square is 324 cm$^2$. Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm$^2$) of the hexagon?
- If the area of a rhombus is $10 \text{ cm}^2$ and one of its interior angles is $150^\circ$, what is the perimeter (in cm) of the rhombus?
- If the area of a rhombus is 10 cm$^2$ and one of its interior angles is 150°, what is the perimeter (in cm) of the rhombus?
