Students in a sixth-grade art class are making a mosaic using tiles in the shape of right triangles. The two sides of each tile that meet to form a right angle are 3 centimeters long and 5 centimeters long. If there are 200 tiles in the mosaic, what is the area of the mosaic?
Area of a Triangle = 0.5 x Base x Height
Therefore the area of one mosaic triangle = 0.5 x 3 x 5 = 7.5
So the area of the whole mosaic is : 7.5 x 200 = 1500cm^2
To find the area of the mosaic, we need to find the area of each individual tile and then multiply it by the total number of tiles.
The area of a right triangle can be calculated using the formula:
Area = (base * height) / 2
In this case, the base of the triangle is 3 cm and the height is 5 cm. Plugging these values into the formula, we get:
Area of one tile = (3 * 5) / 2 = 15 / 2 = 7.5 cm²
Next, we need to multiply the area of one tile by the number of tiles to get the total area of the mosaic. Since there are 200 tiles, the total area of the mosaic is:
Total area of the mosaic = Area of one tile * Number of tiles
= 7.5 cm² * 200
= 1500 cm²
Therefore, the area of the mosaic is 1500 square centimeters.