Room and Tile Dimensions
The room has a length of 8 m and a width of 6 m. The tiles are square with a side length of 40 cm.
Convert room dimensions to centimeters for consistency:
- Length = $8 \text{ m} = 8 \times 100 \text{ cm} = 800 \text{ cm}$
- Width = $6 \text{ m} = 6 \times 100 \text{ cm} = 600 \text{ cm}$
- Tile Side = $40 \text{ cm}$
Calculate Areas
Calculate the area of the room floor:
$ A_{\text{room}} = \text{Length} \times \text{Width} = 800 \text{ cm} \times 600 \text{ cm} = 480000 \text{ cm}^2 $
Calculate the area of a single square tile:
$ A_{\text{tile}} = \text{Side} \times \text{Side} = 40 \text{ cm} \times 40 \text{ cm} = 1600 \text{ cm}^2 $
Calculate Minimum Tiles Required
Divide the total floor area by the area of one tile to find the number of tiles needed without considering wastage.
$ \text{Number of Tiles} = \frac{A_{\text{room}}}{A_{\text{tile}}} = \frac{480000 \text{ cm}^2}{1600 \text{ cm}^2} = 300 \text{ tiles} $
Calculate Total Tiles Including Extra Percentage
An additional 10% of tiles are purchased to account for cutting and potential breakage.
Extra tiles = $10\% \text{ of } 300 = 0.10 \times 300 = 30 \text{ tiles}$
Total tiles needed = Tiles for coverage + Extra tiles
$ \text{Total Tiles} = 300 + 30 = 330 \text{ tiles} $
Similar Questions
- An L-shaped floor is made of two rectangles (6 m $\times$ 4 m and 8 m $\times$ 6 m). Tiles cost ₹450/$m^2$, but a 10% discount is given if more than 70 $m^2$ is tiled. What is the total cost after discount?
- A large regular polygon is made by combining 6 regular hexagons around a common center. What is the ratio of area of the combined shape to one hexagon?
- A triangular traffic sign has sides measuring 13 m, 14 m, and 15 m. If the cost to paint the sign is ₹5 per square meter, what will be the total expense to paint the entire sign?
- A triangular field with base 40 m and height 30 m shares a side with a rectangle of length 40 m and breadth 25 m. Find the combined area and percentage of the triangle’s area in the total.
- A regular hexagon is inscribed inside a circle of radius 14 cm. Find the area of the hexagon.
- A steel plate is in the shape of a right triangle. The lengths of the legs are in the ratio 5:12. If the hypotenuse is 13 m, what is the area?
- A triangular flag has base and height in the ratio 5:4. If the area is 160 cm², what are the base and height?
- Consider a right trapezoidal field. Its two parallel sides are 30 meters and 50 meters long. One of its non-parallel sides, which acts as the height, measures 20 meters. What is the area of this field?
- A hexagon is drawn inside a circle with a radius of 21 cm. Determine the approximate area of the hexagon.
- A rectangular field has an area of 600 square meters. If its length were increased by 10 meters and its width decreased by 2 meters, the area of the field would remain the same. Find the original dimensions (length and width) of the field.
Important Questions from 2-D Mensuration
- The sides of a rectangular field are 169 m and 154 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field? Take $\pi = \frac{22}{7}$
- Find the area of a sector with a central angle of 150° in a circle with a radius of 12 cm.
- The area of a square is $2304$ cm$^2$. Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm$^2$) of the hexagon?
Calculate the area of the triangle whose sides are 8 cm, 9 cm and 13 cm. (Rounded up to two decimal places)
- The length of a rectangular pitch is 30 m more than its breadth. Its area is $18,271$ m$^{2}$. Its breadth (in m) is:
