A patio has the shape of the quadrilateral drawn in the picture below.
1) Find the area of the patio.
2) What is the minimum number of square-tiles with sides of 30 cm that are needed to cover the patio if 10% more tiles will be needed to cover the non-rectangular shape of the patio?
it is 550 tiles!
your welcome!
45 meters is also correct
the area is 45 meters squared
To find the area of the patio, we need to determine the area of the quadrilateral shape shown in the picture.
1) Area of the patio:
In order to find the area of the patio, we can divide it into two rectangles and a triangle. Let's calculate the area of each shape separately:
Rectangle 1:
To find the area, we multiply the length and width of the rectangle.
Length = 12m
Width = 6m
Area of Rectangle 1 = Length * Width = 12m * 6m = 72m²
Rectangle 2:
Length = 6m
Width = 3m
Area of Rectangle 2 = Length * Width = 6m * 3m = 18m²
Triangle:
To find the area of the triangle, we use the formula: Area = (base * height) / 2.
Base = 6m
Height = 3m
Area of the triangle = (6m * 3m) / 2 = 9m²
Now, we need to add up the areas of the rectangles and the triangle to get the total area of the patio:
Total area of the patio = Area of Rectangle 1 + Area of Rectangle 2 + Area of the triangle = 72m² + 18m² + 9m² = 99m²
Therefore, the area of the patio is 99 square meters.
2) Number of square-tiles:
To find the minimum number of square-tiles needed to cover the patio, we need to calculate the total area of the patio and take into account the additional 10% for covering the non-rectangular shape.
Total area of the patio = 99m²
Additional 10% = (10/100) * 99m² = 9.9m²
Now, let's calculate the total area of the patio with the additional 10%:
Total area with additional 10% = Total area + Additional 10% = 99m² + 9.9m² = 108.9m²
Since each square-tile has sides of 30cm or 0.3m, we can find the minimum number of tiles by dividing the total area with additional 10% by the area of one tile:
Minimum number of square-tiles = Total area with additional 10% / Area of one tile
Minimum number of square-tiles = 108.9m² / 0.3m²/tile = 363
Therefore, the minimum number of square-tiles with sides of 30cm needed to cover the patio is 363 tiles.