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CBSE Class 9 Answered

The base of a prism is an equilateral triangle of perimeter 12 cm and height is 5 cm .What is it  total surface area. 
Asked by Sreelekshmi2003 | 09 Feb, 2019, 09:15: AM
answered-by-expert Expert Answer
Figure shows the base of prism.  Each side of base triangle is 4 cm, because the triangle is equilateral with perimeter 12 cm.

If O is the center of base area, then OD is half of perpendicular length AD. Hence OD = (√3/4)×4 = √3 cm

If vertical height is 5 cm, then slant height of lateral triangular surfaces is begin mathsize 12px style square root of O D squared plus h squared end root space equals space square root of 3 plus 25 end root space equals space square root of 28 end style cm
Prism has four surfaces : 3 lateral isoceless triangular surfaces + 1 base equilateral triangular surface
 
Area of each lateral surface = begin mathsize 12px style 1 half cross times 4 cross times square root of 28 equals space 2 cross times square root of 28 space end root end style sq. cm
Area of base surface = begin mathsize 12px style 1 half cross times fraction numerator square root of 3 over denominator 2 end fraction cross times 4 cross times 4 space equals space 4 square root of 3 space s q. space c m end style
Total surface area = begin mathsize 12px style 3 cross times 2 cross times square root of 28 space plus space 4 square root of 3 space equals space 12 cross times square root of 7 space plus space 4 square root of 3 space almost equal to space 39 space s q. c m end style
Answered by Thiyagarajan K | 09 Feb, 2019, 09:54: PM

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