Question

1. Find the area of the rhombus having
each side equal to 17 cm and one of its
diagonals equal to 16 cm.​

Answer 1

Answer:

A=1

2p4a2﹣p2

Step-by-step explanation:

Answer 2

$\huge\bf\red{\underline{\underline{Given}}}\::$

• $\sf\orange{AB\: =\: BC\: = \:CD \:=\: DA\: =\: 17 cm}$

• $\sf\orange{AO \:=\: 8 cm}$

• $\sf\orange{AC\: =\: 16 cm}$

$\huge\bf\red{\underline{\underline{To\:Find}}}\::$

• $\sf\gray{Area \: of \: the \: rhombus}$

$\huge\bf\red{\underline{\underline{Solution}}}\::$

$\star\:\sf\underline\orange{In\:\triangle AOD,}$

$\to\:\sf\purple{AD^{2} \: =\: AO^{2}\: + \:OD^{2}}$

$\to\:\sf\green{17^{2}\:= \:8^{2}\: + \:OD^{2}}$

$\to\:\sf\purple{289\: = \:64\: +\: OD^{2}}$

$\to\:\sf\green{225 \:= \:OD^{2}}$

$\to\:\sf\purple{OD\:=\:15}$

$\hookrightarrow\:\sf\pink{BD\:= \:2 \:\times\:OD}$

$\hookrightarrow\:\sf\purple{BD\:=\:2\:\times\:15}$

$\hookrightarrow\:\sf\pink{BD\:=\:30cm}$

$\star\:\sf\underline\red{Now,\: Finding\:the\:area\:of\: rhombus}$

$\mapsto\:\sf\orange{Area_{\:(Rhombus)}\:=\:\dfrac{1}{2}\:\times\:d_{1}\:\times\:d_{2}}$

$\mapsto\:\sf\blue{Area_{\:(Rhombus)}\:=\:\dfrac{1}{2}\:\times\:16\:\times\:30}$

$\mapsto\:\underline{\boxed{\sf{\orange{Area_{\:(Rhombus)}\:=\:240cm^{2} } }}}$