Question

. In the given figure how many triangles are there with A as one vertex

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Answer 1

Answer:

I don't know

Step-by-step explanation:

Answer 2

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ʟᴇᴛ ᴜꜱ ᴄᴏᴜɴᴛ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ᴛʀɪᴀɴɢʟᴇꜱ ᴠᴇʀᴛᴇx ᴡɪꜱᴇ.

ғʀᴏᴍ ᴠᴇʀᴛᴇx 1, ᴡᴇ ᴄᴀɴ ᴄᴏᴜɴᴛ 4 ᴛʀɪᴀɴɢʟᴇꜱ.

ғʀᴏᴍ ᴠᴇʀᴛɪᴄᴇꜱ 2 ᴀɴᴅ 3, ᴡᴇ ᴄᴀɴ ᴄᴏᴜɴᴛ 3 ᴛʀɪᴀɴɢʟᴇꜱ ᴇᴀᴄʜ.

ғʀᴏᴍ ᴠᴇʀᴛɪᴄᴇꜱ 4,5,6, ᴡᴇ ʜᴀᴠᴇ 2 ᴛʀɪᴀɴɢʟᴇꜱ ᴇᴀᴄʜ.

ғɪɴᴀʟʟʏ, ғʀᴏᴍ ᴠᴇʀᴛɪᴄᴇꜱ, 7,8,9,10, ᴡᴇ ʜᴀᴠᴇ 1 ᴛʀɪᴀɴɢʟᴇ ᴇᴀᴄʜ.

ᴡᴇ ᴛʜᴜꜱ ʜᴀᴠᴇ 4×1+3×2+2×3+1×4=40 ᴛʀɪᴀɴɢʟᴇꜱ.

ᴛʜᴇꜱᴇ ᴀʀᴇ ʜᴏᴡᴇᴠᴇʀ, ᴜᴘʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇꜱ ᴏɴʟʏ.

ғʀᴏᴍ ᴠᴇʀᴛɪᴄᴇꜱ 12,13,14 ᴡᴇ ʜᴀᴠᴇ 1+2+1=4 ᴛʀɪᴀɴɢʟᴇꜱ ɪɴ ɪɴᴠᴇʀᴛᴇᴅ ꜱʜᴀᴘᴇꜱ.

ғʀᴏᴍ 8,9, ᴡᴇ ʜᴀᴠᴇ 1 ᴛʀɪᴀɴɢʟᴇ ᴇᴀᴄʜ ᴀɴᴅ ғʀᴏᴍ 5, ᴡᴇ ʜᴀᴠᴇ 1 ᴛʀɪᴀɴɢʟᴇ.

ᴛʜᴜꜱ, ᴛᴏᴛᴀʟ ɴᴏ. ᴏғ ɪɴᴠᴇʀᴛᴇᴅ ᴛʀɪᴀɴɢʟᴇꜱ =7

ʜᴇɴᴄᴇ, ᴛᴏᴛᴀʟ ɴᴏ. 20+7=27

ᴇxᴛᴇɴᴅɪɴɢ ᴛʜɪꜱ ᴘᴀᴛᴛᴇʀɴ ᴏғ ᴄᴏᴜɴᴛɪɴɢ, ʟᴇᴛ ᴜꜱ ᴄᴏᴜɴᴛ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇꜱ ɪɴ ғɪɢ.

ᴜᴘʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇꜱ =5×1+4×2+3×3+2×4+1×5=35

ɪɴᴠᴇʀᴛᴇᴅ ᴛʀɪᴀɴɢʟᴇꜱ =(1+2+2+1)+(1+2+1)+(1+1)+1=13

ʜᴇɴᴄᴇ ᴛᴏᴛᴀʟ ɴᴜᴍʙᴇʀ =48