Nikolai is installing an L-shaped desk. What is the surface of the desktop if it is 1 in thick 40in height 55inches wide 35 inches length 22inchesheight
The L-shaped desk has two parts: a rectangular part and a triangular part.
Surface of rectangular part = length x width = 35in x 55in = 1925 sq in
Surface of triangular part = 1/2 x base x height = 1/2 x 22in x (40in - 1in - 1in) = 420 sq in
Total surface area of the desktop = surface of rectangular part + surface of triangular part
= 1925 sq in + 420 sq in
= 2345 sq in
Therefore, the surface of the desktop is 2345 square inches.
To calculate the surface area of an L-shaped desk, we need to break down the shape into separate components and calculate their areas individually.
1. Calculate the area of the main rectangular section:
- Length: 35 inches
- Width: 55 inches
- Height: 1 inch (we will account for this later)
The surface area of a rectangular prism is given by the formula: Area = Length x Width.
Therefore, the area of the main rectangular section is: 35 inches x 55 inches = 1925 square inches.
2. Calculate the area of the smaller rectangular section:
- Length: 22 inches
- Width: 1 inch (thickness)
- Height: 40 inches
The surface area of a rectangular prism is given by the formula: Area = Length x Width.
Therefore, the area of the smaller rectangular section is: 22 inches x 40 inches = 880 square inches.
3. Subtract the overlapping area:
As the smaller rectangular section is attached to one side of the main rectangular section, there will be an overlapping area between them. This overlapping area has a width of 1 inch (thickness) and a height of 40 inches.
The overlapping area is given by the formula: Area = Length x Width.
Therefore, the overlapping area is: 1 inch x 40 inches = 40 square inches.
4. Calculate the total surface area:
To get the total surface area of the L-shaped desk, we need to add the area of the main rectangular section, the area of the smaller rectangular section, and then subtract the overlapping area.
Total surface area = (Area of main section + Area of smaller section) - Overlapping area
Total surface area = (1925 square inches + 880 square inches) - 40 square inches
Total surface area = 2805 square inches - 40 square inches
Total surface area = 2765 square inches.
Therefore, the surface area of the L-shaped desk is 2765 square inches.