Question

a shape composed of two rectangular prisms is shown. what is the surface area of the composite figure? enter your answer in the box. 222 square centimeters

Explanation:

Step1: Calculate the surface area of the larger rectangular prism

The formula for the surface area of a rectangular prism is \(2(lw + lh+ wh)\). For the larger part (assuming length \(l = 9\)cm, width \(w = 3\)cm, height \(h = 7\)cm), but we need to adjust for the overlapping part. The overlapping area is \(3\times3\) (since the smaller prism has width and height \(3\)cm).
The front - back area of the larger part: \(2\times(9\times3)=54\)
The left - right area: \(2\times(3\times7) = 42\)
The top - bottom area: \(2\times(9\times7)=126\). But we subtract \(2\times(3\times3)\) (because of the overlapping with the smaller prism). So the adjusted surface area of the part related to the larger prism: \((54 + 42+126)- 18=204\)

Step2: Calculate the surface area of the smaller rectangular prism

The smaller prism has length \(l = 6\)cm, width \(w = 3\)cm, height \(h = 3\)cm. But we only consider the non - overlapping faces. The two side faces: \(2\times(3\times3)=18\)

Step3: Sum up the surface areas

Add the relevant areas from the two prisms: \(204 + 18=222\)

Answer:

\(222\) square centimeters