a We know that the solids are similar. In a prism the base areas are congruent shapes, so we can identify corresponding sides in our solids.
In similar shapes the ratio of corresponding sides are the same. With this information we can write two equations.
y/10=6/8 and x/9=8/6
Let's solve these equations.
b We want to determine the ratio of corresponding sides of Solid B to Solid A. This means we should divide a side in Solid B with its corresponding side in Solid A. From Part A, we identified that the 8 units side in Solid B corresponds to the side in Solid A that is 6 units.
8/6 ⇔ 4/3
c To find the area of a shape given the area of a similar shape, we should multiply the given area by the area scale factor between the shapes. This is equal to the square of the Linear scale factor.
Area scale factor=(Linear scale factor)^2From Part B, we know that the linear scale factor between the solids is 43. With this information we can determine the area scale factor.
Now we can find the base area of solid B by multiplying the base area of Solid A by the area scale factor.
27(16/9)=48
The base area of Solid B is 48 square units.
