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Hᴇʀᴇ's Yᴏᴜʀ Aɴsᴡᴇʀ:-
Gɪᴠᴇɴ:
• ABCDE ɪs ᴀ Pᴏʟʏɢᴏɴ
Tᴏ Fɪɴᴅ:
• Aʀᴇᴀ ᴏғ Tʜᴇ Pᴏʟʏɢᴏɴ
Fʀᴏᴍ Tʜᴇ Fɪɢᴜʀᴇ:
Tʜᴇʀ Aʀᴇ Tʜʀᴇᴇ Tʀɪᴀɴɢʟᴇs ɪɴ Tʜᴇ Gɪᴠᴇɴ Fɪɢᴜʀᴇ ᴏғ Pᴏʟʏɢᴏɴ
Nᴀᴍᴇs ᴏғ Tʀɪᴀɴɢʟᴇs:
- △ABE
- △DCE
- △BEC
Sᴏʟᴜᴛɪᴏɴ:
Iɴ △ABE,
AB = 8ᴍ
AE = 8ᴍ
BE = 12ᴍ
S = a + b + c / 2
⇏S = 8 + 8 + 12 / 2 m
⇏S = 14 m
Nᴏᴡ Aᴄᴄᴏʀᴅɪɴɢ ᴛᴏ Hᴇʀᴏɴ's Fᴏʀᴍᴜʟᴀ
Aʀᴇᴀ = √s ( s - a )( s - b )( s - c) sǫ.ᴜɴɪᴛs
Aʀᴇᴀ = √14 × 6 × 6 × 2 ᴍ^2
= 6 √ 2 × 7 × 2 ᴍ^2
= 12√7 ᴍ^2
= 12 × 2.64 ᴍ^2
= 31.68 ᴍ^2
Iɴ △CED,
CE = 12ᴍ
CD = 10ᴍ
DE = 10ᴍ
S = 12 + 10 + 10 /2
= 16ᴍ
Aᴄᴄᴏʀᴅɪɴɢ ᴛᴏ Hᴇʀᴏɴ's Fᴏʀᴍᴜʟᴀ
Aʀᴇᴀ = √ 16( 16 - 10 )( 16 - 10 )( 16 - 12 )
= √ 16 × 6 × 6 × 4 ᴍ^2
= 24 × 2 ᴍ^2
= 48 ᴍ^2
Iɴ △BEC,
BC = 8ᴍ
CE = 12ᴍ
BE = 12ᴍ
S = 8 + 12 + 12/2
= 16 ᴍ
Aᴄᴄᴏʀᴅɪɴɢ ᴛᴏ Hᴇʀᴏɴ's Fᴏʀᴍᴜʟᴀ
Aʀᴇᴀ = √ 16 ( 16 - 8 )( 16 - 12 )( 16 - 12 )
= √ 16 × 8 × 4 × 4
= 32√2 ᴍ^2
= 32 × 1.41 ᴍ^2
= 45.12 ᴍ^2
Aʀᴇᴀ ᴏғ Pᴏʟʏɢᴏɴ = Sᴜᴍ ᴏғ Aʀᴇᴀ ᴏғ Aʟʟ Tʜʀᴇᴇ Tʀɪᴀɴɢʟᴇs
= ( 31.68 + 48 + 45.12 ) ᴍ^2
= 124.8 ᴍ^2
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