Question

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.

Plz plz plz plz help me
Give me correct answer please

Answer 1

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.

HOPE IT HELPS YOU OUT

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Answer 2

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.