To draw the diagonal of following polygons
1 quadrilaterals
2 pentagon
3 hexagon
4 heptagon
5 octagon and hence derive the formula for finding the number of diagonals in polygon.
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Give me correct answer please
Answers
Step-by-step explanation:
ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ᴅɪᴀɢᴏɴᴀʟs ɪɴ ᴀ ᴘᴏʟʏɢᴏɴ = ɴ(ɴ-3)/2, ᴡʜᴇʀᴇ ɴ ɪs ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ᴘᴏʟʏɢᴏɴ sɪᴅᴇs.
ғᴏʀ ᴀ ᴄᴏɴᴠᴇx ɴ-sɪᴅᴇᴅ ᴘᴏʟʏɢᴏɴ, ᴛʜᴇʀᴇ ᴀʀᴇ ɴ ᴠᴇʀᴛɪᴄᴇs, ᴀɴᴅ ғʀᴏᴍ ᴇᴀᴄʜ ᴠᴇʀᴛᴇx ʏᴏᴜ ᴄᴀɴ ᴅʀᴀᴡ ɴ-3 ᴅɪᴀɢᴏɴᴀʟs, sᴏ ᴛʜᴇ ᴛᴏᴛᴀʟ ɴᴜᴍʙᴇʀ ᴏғ ᴅɪᴀɢᴏɴᴀʟs ᴛʜᴀᴛ ᴄᴀɴ ʙᴇ ᴅʀᴀᴡɴ ɪs ɴ(ɴ-3). ʜᴏᴡᴇᴠᴇʀ, ᴛʜɪs ᴡᴏᴜʟᴅ ᴍᴇᴀɴ ᴛʜᴀᴛ ᴇᴀᴄʜ ᴅɪᴀɢᴏɴᴀʟ ᴡᴏᴜʟᴅ ʙᴇ ᴅʀᴀᴡɴ ᴛᴡɪᴄᴇ, (ᴛᴏ ᴀɴᴅ ғʀᴏᴍ ᴇᴀᴄʜ ᴠᴇʀᴛᴇx), sᴏ ᴛʜᴇ ᴇxᴘʀᴇssɪᴏɴ ᴍᴜsᴛ ʙᴇ ᴅɪᴠɪᴅᴇᴅ ʙʏ 2.
EG -
ʜᴇxᴀɢᴏɴ (6 sɪᴅᴇs)
(6² - 3(6))/2
(36 - 18)/2
18/2
ᴛʜᴇʀᴇ ᴀʀᴇ 9 ᴅɪᴀɢᴏɴᴀʟs.
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Answer:
The number of diagonals of an n-sided polygon is:
n(n − 3) / 2
Examples:
a square (or any quadrilateral) has 4(4−3)/2 = 4×1/2 = 2 diagonals
an octagon has 8(8−3)/2 = 8×5/2 = 20 diagonals.
a triangle has 3(3−3)/2 = 3×0/2 = 0 diagonals.
