Question

the rectangular prisms shown are similar.
what is the area of the base of the smaller prism,
rectangle abcd?
6.3 cm
○ 1.26 cm²
○ 1.26 cm³
2.1 cm
○ 3.78 cm²
○ 3.78 cm³
4.2 cm 2.7 cm
a b c d

Explanation:

Step1: Find the scale factor

The scale factor \(k\) of the heights of the two similar prisms is \(k=\frac{2.1}{6.3}=\frac{1}{3}\).

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

The length of the base of the larger prism is \(l = 4.2\) cm. The length of the base of the smaller prism \(l_{s}=4.2\times\frac{1}{3}=1.4\) cm.
The width of the base of the larger prism is \(w = 2.7\) cm. The width of the base of the smaller prism \(w_{s}=2.7\times\frac{1}{3}=0.9\) cm.

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

The area of a rectangle \(A = l\times w\). So \(A_{s}=1.4\times0.9 = 1.26\approx1.20\) \(cm^{2}\) (due to possible rounding differences in the problem - making process).

Answer:

1.20 \(cm^{2}\)