1. 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 ΔDAB = 90°. If the volume of the prism be 2070 cm3, then the area of the lateral surface is
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By: anil on 05 May 2019 01.53 am
In right $$ riangle$$DAB, using Pythagoras theorem, => $$BD = sqrt{(AD)^2 + (AB)^2}$$ => $$BD = sqrt{12^2 + 9^2} = sqrt{225}$$ => $$BD = 15 cm$$ Now, area of $$ riangle$$DAB = $$frac{1}{2} * 9 * 12 = 54 cm^2$$ Area of $$ riangle$$BCD = $$sqrt{s(s-a)(s-b)(s-c)}$$ where, $$s = frac{a+b+c}{2}$$ => Area of $$ riangle$$BCD = $$sqrt{21 * 6 * 7 * 8} = 84 cm^2$$ => Area of quad ABCD = area of $$ riangle$$DAB + area of $$ riangle$$BCD = 54+84 = $$138 cm^2$$ Volume of prism = base area * height => 2070 = 138 * height => height = 15 cm Lateral surface area of prism = perimeter of base * height = (12 + 9 + 14 + 13) * 15 = 48 * 15 = 720 $$cm^2$$
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