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The base of a right prism is a pentagon whose sides are in the ratio 1 : √2 : √2 : 1 : 2 and its height is 10 cm. If the longest side of the base be 6 cm, the volume of the prism is 

(a) 270 cm3 

(b) 360 cm3 

(c) 540 cm3 

(d) None of these

1 Answer

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Best answer

(a) 270 cm3

The base of the prism is a pentagon as shown. 

If the longest side is 6 cm, then the other sides are 3 cm, 3√2 cm, 3√2 cm, 3 cm 

Since ABC is an isosceles triangle, AF ⊥ BC and ∠AFB = 90º. 

∴ BF = FC = 3 cm 

In ΔABF, AF = \(\sqrt{(3\sqrt2)^2-3^2}=\sqrt{18-9}=\sqrt9=3.\)

∴ Total area of the base = Area of ΔABC + Area of rect. BCDE 

= \(\big(\frac12\times6\times3+6\times3\big)\) cm2 = (9+18) cm= 27 cm2.

∴ Volume of prism = Area of base × height 

= (27 × 10) cm3 = 270 cm3.

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