Two views of a trapezoidal prism are shown below.
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Each square on this grid has an area of one square centimetre.
The vertical edges of the prism are 4 centimetres.
- What is the area of the shaded cross-section in square centimetres? (2 marks)
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- What is the volume of the prism in cubic centimetres? (2 marks)
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Show Worked Solution
a. \(\text{The area of the cross-section (trapezium)}\)
\(=12\ \text{squares}+9\ \text{triangles}\ (1\times 1) + 1\ \text{triangle}\ (1\times 3)\)
\(=12+(9\times \dfrac{1}{2})+1\dfrac{1}{2}\)
\(=18\ \text{cm}^2\)
| b. | \(\text{Volume}\) | \(=Ah\) |
| \(=18\times 4\) | ||
| \(=72\ \text{cm}^3\) |