What is the volume of a right prism standing on a triangular base of sides 5 cm, 5 cm and 8 cm whose lateral surface area is 828 cm^2 ? -Maths 9th

What is the volume of a right prism standing on a triangular base of sides 5 cm, 5 cm and 8 cm whose lateral surface area is 828 cm^2 ? -Maths 9th
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Answer :

Lateral surface area of a prism = Perimeter of base × Height  ⇒ 840 = (5 + 5 + 8) × Height  ⇒ Height = 8401884018 = 46 cm. = Semi perimeter of the triangular base = 182182 = 9 cm ∴ Area of triangle = 9(9–5)(9–5)(9–8)−−−−−−−−−−−−−−√9(9–5)(9–5)(9–8)     (Herons Formula) = 9×4×4×1−−−−−−−−−−√9×4×4×1 = 12 cm2  ∴ Required volume of prism = Area of base × Height  = (12 × 46) cm3 = 552cm3
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