Question

ꜰɪɴᴅ ᴛʜᴇ ᴀʀᴇᴀꜱ ᴏꜰ ᴛʜᴇ ꜰɪɢᴜʀᴇꜱ ɢɪᴠᴇɴ ʙᴇʟᴏᴡ :-​

Answer 1

Answer:

area of first figure= 76

area of second figure=200

Answer 2

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

ꜰɪɴᴅ ᴛʜᴇ ᴀʀᴇᴀꜱ ᴏꜰ ᴛʜᴇ ꜰɪɢᴜʀᴇꜱ ɢɪᴠᴇɴ ʙᴇʟᴏᴡ :-

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf \huge {iii}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\sf \bf {ABCD \:is \:a\: square}$
• $\sf \bf {AFE\: and\: DGH\: are \:triangles}$
• $\sf \bf {AB=BC=CD=DA=8cm}$
• $\sf \bf {FE=GH=4cm}$
• $\sf \bf {AE=DH=5cm}$
• $\sf \bf {AF=DG=4cm}$

$\sf \bf (AF=AB-FB\\=8-4 \\AF=4cm) \\\\ (DG=DC-GC\\=8-4\\DG=4cm)$

$\sf \bf {\boxed {\mathbb {TO\:PROVE}}}$

• $\sf \bf {Area \:of \:the\: total\: figure}$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

$\sf \bf {Area\: of\: the\: square}$

$\sf \bf {\boxed {\color{blue} {A={a}^{2}}}}$

• $\sf \bf {A=area\: of \:the \:square}$
• $\sf \bf {a=side\: of \:a\: square}$

$\sf \bf {Substitute \:the\: values}$

$\sf \bf \implies A={8}^{2}$

$\sf \bf \implies {\boxed {\color{red} {A=64 {cm}^{2}}}}$

$\sf \bf {Area\: of\: the\: 2 \:triangles}$

$\sf \bf {\boxed {\color{blue} {A=\dfrac{1}{2} \times b \times h}}}$

• $\sf \bf {A=area\: of \:the \:triangle}$
• $\sf \bf {h=height }$
• $\sf \bf {b=breadth}$

$\sf \bf {Substitute \:the\: values}$

$\sf \bf \implies A=\cancel{2}\dfrac{1}{\cancel {2}} \times 4 \times 4$

$\sf \bf \implies A=4 \times 4$

$\sf \bf \implies {\boxed {\color{red} {A=16{cm}^{2}}}}$

$\sf \bf {Total\: area\: of\: the\: figure}$

$\sf \bf \implies A=64+16$

$\sf \bf \implies {\boxed {\boxed {\color{green} {A=80{cm}^{2}}}}}$

_______________________________________ _______________________________________

$\sf \bf \huge {iv}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\sf \bf {ABCD \:is \:a\: rectangle}$
• $\sf \bf {AFG\:,\: DFG\:, \:BEH\:, \:CEH\:are \:triangles}$
• $\sf \bf {AB=CD=15cm}$
• $\sf \bf {BC=DA=10cm}$
• $\sf \bf {FG=EH=5cm}$

$\sf \bf {\boxed {\mathbb {TO\:PROVE}}}$

• $\sf \bf {Area \:of \:the\: total\: figure}$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

$\sf \bf {Area\: of\: the\: rectangle}$

$\sf \bf {\boxed {\color{blue} {A=l \times b}}}$

• $\sf \bf {A=area\: of \:the \:rectangle}$
• $\sf \bf {l=length}$
• $\sf \bf {b=breadth}$

$\sf \bf {Substitute \:the\: values}$

$\sf \bf \implies {A=10 \times 15}$

$\sf \bf \implies {\boxed {\color{red}{A= 150{cm}^{2}}}}$

$\sf \bf {Area\: of\: the\: 4 \:triangles}$

$\sf \bf {\boxed {\color{blue} {A=\dfrac{1}{2} \times b \times h}}}$

• $\sf \bf {A=area\: of \:the \:triangle}$
• $\sf \bf {h=height }$
• $\sf \bf {b=breadth}$

$\sf \bf {Substitute \:the\: values}$

$\sf \bf \implies A=4\dfrac{1}{2} \times 5 \times 5$

$\sf \bf \implies A=2 \times 5 \times 5$

$\sf \bf \implies {\boxed {\color{red} {A=50{cm}^{2}}}}$

$\sf \bf {Total\: area\: of\: the\: figure}$

$\sf \bf \implies A=150+50$

$\sf \bf \implies {\boxed {\boxed {\color{green} {A=200{cm}^{2}}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU }}}$

__________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

• $\sf \bf {Area\: of \:the \:triangle=\dfrac{1}{2} \times b \times h}$

• $\sf \bf {Area\: of \:the \:Square ={a}^{2}}$

• $\sf \bf {Area\: of \:the \:rectangle = l\times b }$

• $\sf \bf {Area\: of \:the \: parallelogram= B \times h}$

• $\sf \bf {Area\: of \:the \:rhombus = \dfrac{d_1 \times d_2}{2}}$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$