The sides of a base of a prism are 12cm,16cm,20cm and it's height is 15cm then it's volume is
Answers
Ans: 720 cubic cms
step by step explanation
it is triangular prism with sides 12cm,16cm,20cm
S = 12 + 16 + 20= 48/2 =24
Area of the triangle =√s(s-a) (s - b)(s - c)
= √24(24 -12)(24 -16)(24 -20)
=√24(12)(8)(4)=√(12)(2)(12)(2)(4)(4)
= 12 x 2 x4 =96 sq cms
Volume of the prism =1/2 Area of the
base x height
= 1/2 (96)(15) =(48)(15)=
720 cubic cms
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Question :- The sides of base of a triangular Prism are 12cm, 16cm and 20cm. If its height is 15cm, Find its volume ?
Solution :-
we have given that, sides of base of a triangular Prism are 12cm, 16cm and 20cm.
So,
→ Perimeter of base = (12 + 16 + 20) = 48 cm.
→ Semi - Perimeter = 48/2 = 24 cm.
then,
→ Area of base = √[s*(s-a)*(s-b)*(s-c) , where s is semi - perimeter and a , b and c are length of sides of ∆ .
→ Area of base = √[24 * (24 - 12) * (24 - 16) * (24 - 20)]
→ Area of base = √(24 * 12 * 8 * 4)
→ Area of base = √(2 * 12 * 12 * 2 * 4 * 4)
→ Area of base = √(2² * 12² * 4²)
→ Area of base = 2 * 12 * 4
→ Area of base = 96 cm².
now, we know that,
- Volume of Prism = Area of Base * Height
therefore,
→ Volume = 96 * 15
→ TSA = 1440 cm³. (Ans.)
Hence, Volume of Prism will be 1440 cm³.
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