Question

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what is the area of a cross section that is parallel to face cdhg?
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\boxed{} cm²
(image of a rectangular prism with dimensions: ad = 6 cm, dc = 12 cm, cg = 36 cm)

Explanation:

Step1: Identify the shape and dimensions of the cross - section

Since the cross - section is parallel to face \(CDHG\), the cross - section is a rectangle. The dimensions of the rectangle are the same as the dimensions of face \(CDHG\). The height of the rectangle is \(6\mathrm{cm}\) (same as \(AD\)) and the length of the rectangle is \(36\mathrm{cm}\) (same as \(HG\)).

Step2: Calculate the area of the rectangle

The area formula for a rectangle is \(A = l\times w\), where \(l\) is the length and \(w\) is the width. Substituting \(l = 36\mathrm{cm}\) and \(w = 6\mathrm{cm}\) into the formula, we get \(A=36\times6\).

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Answer:

\(216\)