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The base of a right prism is a quadrilat...

The base of a right prism is a quadrilateral ABCD. Given that AB = 9 cm, BC = 14 cm, CD = 13 cm, DA = 12 cm and `angleDAB = 90^(@)`. If the volume of the prism be `2070 cm^(3)`, then the area of the lateral surface is

A

720 वर्ग सेमी

B

810 वर्ग सेमी

C

1260 वर्ग सेमी

D

2070 वर्ग सेमी

Text Solution

Verified by Experts

The correct Answer is:
A

`DeltaABD `का क्षेत्रफल
`= 1/2 xx 9 xx 12 = 54 cm^2`
`BD = sqrt(12^2 + 9^2) = 15 cm`
`therefore Delta BCD` का क्षेत्रफल `= sqrt(21 xx 6 xx 7 xx 8) = 84 cm^2`
`square ABCD `का क्षेत्रफल = `54 + 84 = 138cm^2`
प्रिज्म का आयतन = 2070
`implies 138 xx x = 2070` (x = ऊँचाई)
`implies x = (2070)/138 cm`
`therefore` पार्श्व पृष्ठ का क्षेत्रफल `= (9 + 13 + 14 + 12) xx (2070)/138`
`=720cm^2`
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