Calculate Tiles Needed: 3m × 2m Tiles in 10m × 6m Deltoid Pattern

Let's solve the problem step by step:

• Calculate the area of the rectangular garden:
  The garden has a length of 10 meters and a width of 6 meters. Thus, the area is given by: $\text{Area of rectangle} = 10 \, \text{m} \times 6 \, \text{m} = 60 \, \text{m}^2.$

• Consider the deltoid shape:
  The provided image suggests the deltoid is inscribed within the rectangle. If we assume the deltoid is two congruent triangles making up part of the rectangle, let's find the area of each triangle.

• Area of each triangle of the deltoid:
  Assume two symmetrical triangles split the rectangle, each covering 30 m² (half of the rectangle). Hence, the deltoid area is the total area: $\text{Area of deltoid} = \frac{60}{2} \, \text{m}^2 = 30 \, \text{m}^2.$

• Calculate the area of one tile:
  The tile dimensions are 3 meters by 2 meters, so the area is: $\text{Area of one tile} = 3 \, \text{m} \times 2 \, \text{m} = 6 \, \text{m}^2.$

• Determine the number of tiles needed:
  Divide the deltoid's area by the area of one tile: $\text{Number of tiles} = \frac{30 \, \text{m}^2}{6 \, \text{m}^2} = 5.$

Therefore, the number of tiles needed to complete the deltoid shape is 5.