Question

Area of midpoint of parallelogram is equal to half of the area of parallelogram,

Answer 1

$\huge\bf\red{ɢɪᴠᴇɴ :}$

ᴛʜᴇ ʙᴀꜱᴇ ᴏꜰ ᴛʜᴇ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ ɪꜱ ᴛʜʀɪᴄᴇ ɪᴛꜱ ʜᴇɪɢʜᴛ.

ᴀʀᴇᴀ ᴏꜰ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ = 867 ᴄᴍ²

$\huge\bf\red{Tᴏ Fɪɴᴅ :}$

ᴛʜᴇ ʜᴇɪɢʜᴛ.

ᴛʜᴇ ʙᴀꜱᴇ.

$\huge\bf\red{Sᴏʟᴜᴛɪᴏɴ : }$

ʜᴇɴᴄᴇ,ɪᴛ ɪꜱ ɢɪᴠᴇɴ ᴛʜᴀᴛ ᴛʜᴇ ʙᴀꜱᴇ ᴏꜰ ᴛʜᴇ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ ɪꜱ ᴛʜʀɪᴄᴇ ɪᴛꜱ ʜᴇɪɢʜᴛ.

ʟᴇᴛ'ꜱ ꜰɪʀꜱᴛ ᴄᴏɴꜱɪᴅᴇʀ ᴛʜᴇ ʜᴇɪɢʜᴛ ᴏꜰ ᴛʜᴇ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ ʙᴇ x ᴛʜᴇɴ ᴛʜᴇ ʙᴀꜱᴇ ᴡɪʟʟ ʙᴇ 3×x = 3x

Now,

${\underline{\boxed{\sf{\blue{Area_{(parallelogram)}=base\times{height}}}}}}$

$\dashrightarrow\sf{867=3x\times{x}}$

$\dashrightarrow\sf{867=3x^2}$

$\dashrightarrow\dfrac{\cancel{867}^{289}}{\cancel{3}^1}\sf{=x^2}$

$\dashrightarrow\sf{289=x^2}$

$\dashrightarrow\sf{x=\sqrt{289}}$

$\dashrightarrow\sf{x=\sqrt{17\times{17}}}$

$\bigstar\underline{\boxed{\sf{\pink{x=17}}}}$

${\text{\sf{Therefore,the Height (x) is 17cm}}}$

${\text{\sf{And the Base (3x)}}}\sf{= 3\times{17}=51 cm.}$