Question

Q.12
+4
If the sides of a rhombus are 12 cm
and one of its diagonals is 16 cm
then find the area of the rhombus.​

Answer 1

Answer:

Rhombus

Solve for area

A≈143.11cm²

a Side

12

cm

p Diagonal

16

cm

Answer 2

Answer:

Given :-

side of a Rhombus =12cm

Length of one diagonal =16cm

To find:-

Area of Rhombus

Solution:-

Let the other diagonal be x

As we know that in a Rhombus

$\boxed{\sf Side=\dfrac {\sqrt {d_1 {}^2+d_2 {}^2}}{2}}$

• Substitute the values

$\qquad\qquad\displaystyle {:}\longrightarrow 12=\dfrac {\sqrt {16^2+x^2}}{2}$

$\qquad\qquad\displaystyle {:}\longrightarrow 12×2={\sqrt {256+x^2}}$

$\qquad\qquad\displaystyle {:}\longrightarrow 24=\sqrt{256+x^2}$

$\qquad\qquad\displaystyle {:}\longrightarrow 256+x^2=\sqrt {24}$

$\qquad\qquad\displaystyle {:}\longrightarrow x^2=\sqrt {24}-256$

$\qquad\qquad\displaystyle {:}\longrightarrow x^2=256-4.8$

$\qquad\qquad\displaystyle {:}\longrightarrow x^2=251.2$

$\qquad\qquad\displaystyle {:}\longrightarrow x=\sqrt {251.2}$

$\qquad\qquad\displaystyle {:}\longrightarrow x=15.8$

• The other diagonal is 15.8 cm

Now ,

We know that in a Rhombus

$\boxed {\sf Area_{(Rhombus)}=\dfrac {1}{2}×d_1×d_2}$

• Substitute the values

$\qquad\qquad\displaystyle {:}\longrightarrow Area_{(Rhombus)}=\dfrac {1}{\cancel {2}}×\cancel {16}×15.8$

$\qquad\qquad\displaystyle {:}\longrightarrow Area_{(Rhombus)}=8×15.8$

$\qquad\qquad\displaystyle {:}\longrightarrow Area_{(Rhombus)}=126.4cm^2$

$\\\\\therefore\underline{\underline{\sf The\;area\;of\:the\;Rhombus\:is\:126.4cm^2.}}$