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Diketahui luas permukaan limas dengan alas berbent...

Diketahui luas permukaan limas dengan alas berbentuk persegi adalah 96 cm squared. Jika tinggi limas tersebut 4cm maka tentukan kemungkinan luas seluruh bidang tegak limas tersebut?

Jawaban:

Mencari tinggi segitiga pada sisi tegak 

table attributes columnalign right center left columnspacing 0px end attributes row ts equals cell square root of straight t squared plus open parentheses straight s over 2 close parentheses squared end root end cell row blank equals cell square root of 4 squared plus open parentheses straight s over 2 close parentheses squared end root end cell row blank equals cell square root of 16 plus open parentheses straight s over 2 close parentheses squared end root end cell end table

Setelah mencari tinggi segitiga pada sisi tegak limas setelah itu luas permukaan limas dimana:

table attributes columnalign right center left columnspacing 0px end attributes row cell Luas space permukaan space limas space end cell equals cell space luas space alas space plus space 4 left parenthesis luas space bidang space tegak right parenthesis end cell row 96 equals cell straight s squared plus left parenthesis 4 cross times 1 half cross times straight s cross times ts right parenthesis end cell row 96 equals cell straight s squared plus open parentheses 2 cross times straight s cross times square root of 16 plus open parentheses straight s over 2 close parentheses squared end root close parentheses end cell row cell 96 minus straight s squared end cell equals cell 2 straight s square root of 16 plus straight s squared over 4 end root end cell row cell open parentheses 96 minus straight s squared close parentheses squared end cell equals cell open parentheses 2 straight s square root of 16 plus straight s squared over 4 end root close parentheses squared end cell row cell 96 squared minus 192 straight s squared plus straight s to the power of 4 end cell equals cell 4 straight s squared open parentheses 16 plus straight s squared over 4 close parentheses end cell row cell 96 squared minus 192 straight s squared plus straight s to the power of 4 end cell equals cell 4 straight s squared cross times 16 plus 4 straight s squared cross times straight s squared over 4 end cell row cell 96 squared minus 192 straight s squared plus straight s to the power of 4 end cell equals cell 64 straight s squared plus straight s to the power of 4 end cell row cell 96 squared end cell equals cell 64 straight s squared plus 192 straight s squared plus straight s to the power of 4 minus straight s to the power of 4 end cell row cell 96 squared end cell equals cell 256 straight s squared end cell row cell square root of 96 squared end root end cell equals cell square root of 256 straight s squared end root end cell row 96 equals cell 16 straight s end cell row straight s equals cell 96 over 16 end cell row straight s equals cell 6 cm end cell row blank blank blank end table

Setelah mengetahui s barulah mencari kemungkinan luas seluruh bidang tegak limas 

table attributes columnalign right center left columnspacing 0px end attributes row cell Luas space permukaan space limas space end cell equals cell space straight s squared plus luas space seluruh space bidang space tegak space end cell row 96 equals cell 6 squared plus luas space seluruh space bidang space tegak space end cell row 96 equals cell 36 plus luas space seluruh space bidang space tegak space end cell row cell 96 minus 36 end cell equals cell luas space seluruh space bidang space tegak space end cell row 60 equals cell luas space seluruh space bidang space tegak space end cell end table

Jadi kemungkinan luas seluruh bidang tegak limas adalah 60 

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