Question

the rectangular prisms shown are similar. what is the area of the base of the smaller prism, rectangle abcd? 1.26 cm² 1.26 cm³ 3.78 cm² 3.78 cm³

Explanation:

Step1: Find the scale - factor

The ratio of the heights of the two similar prisms is $\frac{2.1}{6.3}=\frac{1}{3}$.

Step2: Find the dimensions of the base of the smaller prism

If the scale - factor is $\frac{1}{3}$, and the dimensions of the base of the larger prism are $4.2$ cm and $2.7$ cm, then the dimensions of the base of the smaller prism are $4.2\times\frac{1}{3}=1.4$ cm and $2.7\times\frac{1}{3}=0.9$ cm.

Step3: Calculate the area of the base of the smaller prism

The area of a rectangle is $A = l\times w$. So, $A=1.4\times0.9 = 1.26$ cm².

Answer:

$1.26$ cm²