Question

Who has given the Cartesian formula?
And also what is heron's formula ??
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Answer 1

Answer:

Question :Who has given the Cartesian formula?

Answer : ʀᴇɴᴇ ᴅᴇsᴄᴀʀᴛᴇs

ᴛʜᴇ ɪɴᴠᴇɴᴛɪᴏɴ ᴏғ ᴄᴀʀᴛᴇsɪᴀɴᴄᴏᴏʀᴅɪɴᴀᴛᴇs ɪɴ ᴛʜᴇ 17ᴛʜ ᴄᴇɴᴛᴜʀʏ ʙʏ ʀᴇɴᴇ ᴅᴇsᴄᴀʀᴛᴇs (ʟᴀᴛɪɴɪᴢᴇᴅ ɴᴀᴍᴇ: ᴄᴀʀᴛᴇsɪᴜs) ʀᴇᴠᴏʟᴜᴛɪᴏɴɪᴢᴇᴅ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄs ʙʏ ᴘʀᴏᴠɪᴅɪɴɢ ᴛʜᴇ ғɪʀsᴛ sʏsᴛᴇᴍᴀᴛɪᴄ ʟɪɴᴋ ʙᴇᴛᴡᴇᴇɴ ᴇᴜᴄʟɪᴅᴇᴀɴ ɢᴇᴏᴍᴇᴛʀʏ ᴀɴᴅ ᴀʟɢᴇʙʀᴀ.

Question :what is heron's formula?

Answer : ɪɴ ɢᴇᴏᴍᴇᴛʀʏ, ʜᴇʀᴏɴ's ғᴏʀᴍᴜʟᴀ (sᴏᴍᴇᴛɪᴍᴇs ᴄᴀʟʟᴇᴅʜᴇʀᴏ's ғᴏʀᴍᴜʟᴀ), ɴᴀᴍᴇᴅ ᴀғᴛᴇʀ ʜᴇʀᴏ ᴏғ ᴀʟᴇxᴀɴᴅʀɪᴀ, ɢɪᴠᴇs ᴛʜᴇ ᴀʀᴇᴀ ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ᴡʜᴇɴ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴀʟʟ ᴛʜʀᴇᴇ sɪᴅᴇs ᴀʀᴇ ᴋɴᴏᴡɴ. ᴜɴʟɪᴋᴇ ᴏᴛʜᴇʀ ᴛʀɪᴀɴɢʟᴇ ᴀʀᴇᴀғᴏʀᴍᴜʟᴀᴇ, ᴛʜᴇʀᴇ ɪs ɴᴏ ɴᴇᴇᴅ ᴛᴏ ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴀɴɢʟᴇs ᴏʀ ᴏᴛʜᴇʀ ᴅɪsᴛᴀɴᴄᴇs ɪɴ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ ғɪʀsᴛ.

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Answer 2

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=> René Descartes

The invention of Cartesian coordinates in the 17th century by René Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra.

=> For a quadrilateral, when one of its diagonal value and the sides are given, the area can be calculated by splitting the given quadrilateral into two triangles and use the Heron's formula. Example :A park, in the shape of a quadrilateral ABCD, has ∠C=90∘, AB = 9 cm, BC = 12 cm, CD = 5 cm and AD = 8 cm.

=> In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle when the length of all three sides are known. Unlike other triangle area formulae, there is no need to calculate angles or other distances in the triangle first.