Volume and Surface Area of a Prism with Trapezium Cross-Section
Volume and Surface Area of a Prism with Trapezium Cross-Section
Secondary 1
The figure shows a solid prism with a trapezium cross-section \(ABCD\). \(AB=5\) cm, \(BC=9\) cm, \(CH=10\) cm, \(FE=3\) cm and \(EH=\sqrt{61}\) cm. Find the
- volume of the prism.
- total surface area of the prism.
Correction to the source diagram: the sloping side is \(\sqrt{5^2+(9-3)^2}=\sqrt{61}\text{ cm}\), approximately \(7.81\text{ cm}\). The printed 8 cm is rounded; use the exact value above in the calculation.
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Answer:(a) \(300\text{ cm}^3\). (b) \((230+10\sqrt{61})\text{ cm}^2\approx308\text{ cm}^2\) (3 s.f.).
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