The sides of base of a triangle are 12cm, 16cm and 20cm. If its height is 15cm, Find L.S.A?
Answers
Correct Question :- The sides of base of a triangular Prism are 12cm, 16cm and 20cm. If its height is 15cm, Find TSA ?
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,
- TSA of Prism = Perimeter * height + 2 * Area of Base
therefore,
→ TSA = 48 * 15 + 2 * 96
→ TSA = 720 + 192
→ TSA = 912 cm². (Ans.)
Hence, TSA of Prism will be 912 cm².
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