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The base of a prism is a right angled triangle with legs 6cm, 8cm and hypotenuse 10cm. If the total surface area of the prism is 156cm2, find its height and its lateral surface area.

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Solution

Given: the base is a right angled triangle with sides a=6cm, b=8cm, c=10cm and T.S.A=156cm2. We know that
T.S.A.=2B+Ph=2×12×8×6+(6+8+10)h=48+24h.
Thus 48+24h=156. This implies that 24h=15648=108.
Hence h=10824=4.5cm.
Therefore LSA=Ph=(6+8+10)×4.5=24×4.5=108cm2.

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