Triangle UVW is the pre-image of triangle RST with a scale factor of 3. Find the area of triangle UVW if the area of triangle RST is 9 cm2.
81 cm^2
To find the area of triangle UVW, we need to know the scale factor between the two triangles and the area of triangle RST.
In this case, we know that the scale factor is 3, and the area of triangle RST is 9 cm².
Since the scale factor is 3, this means that each side of triangle RST is 3 times the length of each corresponding side of triangle UVW.
To find the area of triangle UVW, we can use the following formula:
Area of triangle UVW = (Side of triangle UVW)² * (Area of triangle RST)
Since each side of triangle RST is equal to 3 times each side of triangle UVW, we can substitute this relationship into the formula:
Area of triangle UVW = (Side of triangle UVW)² * (Area of triangle RST)
= (Side of triangle UVW)² * 9 cm²
To isolate the side of triangle UVW, we divide both sides of the equation by 9 and then take the square root:
Area of triangle UVW / 9 cm² = (Side of triangle UVW)²
Taking the square root of both sides:
√(Area of triangle UVW / 9 cm²) = Side of triangle UVW
Now that we know the relationship between the side lengths of the two triangles, we can solve for the side length of triangle UVW:
Side of triangle UVW = √(Area of triangle UVW / 9 cm²)
Since we know that the area of triangle RST is 9 cm², we can substitute this into the equation:
Side of triangle UVW = √(Area of triangle UVW / 9 cm²)
= √(9 cm² / 9 cm²)
= 1 cm
Therefore, each side of triangle UVW is 1 cm.
To find the area of triangle UVW, we substitute the side length into the formula:
Area of triangle UVW = (Side of triangle UVW)² * (Area of triangle RST)
= (1 cm)² * 9 cm²
= 1 cm² * 9 cm²
= 9 cm²
So, the area of triangle UVW is 9 cm².