The two triangles at right are similar.  

1. Find $x$.

   Help (a):

   What would the scale factor be between these two shapes?
   Since $1$ cm is the corresponding side, multiply it by the scale factor to get $x$.

   Answer (a):

   $x=4$ cm

2. Find the area of the smaller triangle.

   Help (b):

   Use the formula for the area of a triangle: $\frac{1}{2}\left(6\ \text{cm}\right)\left(1\ \text{cm}\right)$

3. Based on ratios of similarity, find the area of the large triangle.

   Hint (c):

   When using ratios of similarity to scale a shape, the area of the old shape is multiplied by the scale factor squared to get the area of the new shape.

   Answer (c):

   $3(4)^2=48$ cm²

4. Find the area of the larger triangle by using the formula for the area of a triangle.

   Help (d):

   Use the formula for the area of a triangle: $\frac{1}{2}\left(\text{base}\right)\left(\text{height}\right)$

5. Verify that your answers to (c) and (d) are the same.

   Help (e):

   Did you get the same answer? Make sure to show your work.