Question

The diagonals of a rhombus are 16cm and 12cm.

Find its i) area ii) length of its side​

Answer 1

$\Large{\underbrace{\sf{\red{Required\:Solution:}}}}$

Given,

• The first diagonal of a rhombus = 16 cm and
• The second diagonal of a rhombus = 12 cm

We know that,

$\star\;\boxed{\sf{\purple{Area_{\:(Rhombus)} =\dfrac{1}{2}\Big\lgroup First \:diagonal × Second \:diagonal \Big\rgroup}}}$

$\underline{\bf{\dag} \:\mathfrak{Putting\:values\: :}}$⠀⠀⠀

⠀⠀

$\leadsto\sf Area_{\:(Rhombus)} =\dfrac{1}{2} × First\: diagonal × Second\: diagonal$⠀⠀

$\leadsto\sf Area_{\:(Rhombus)} =\dfrac{1}{2} ×16 × 12 \\\\\\\leadsto \sf Area_{\:(Rhombus)} =6\times 16\\\\\\\leadsto{\underline{\boxed{\frak{Area_{\:(Rhombus)} = 96\; \sf cm^2}}}}$

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2.

• The length of the side a rhombus = $\\\\\bf\sqrt{(\dfrac{D_1}{2} )^2+(\dfrac{D_2}{2} )^2}$

$\\\:\:=\sf\sqrt{8^2+6^2}$

$\\\:\:=\sf\sqrt{64+36}$

$\\\:\:=\sf\sqrt{100}$

$\\\:\:=\sf{10}$

• Hence, the length of the side a rhombus is 10 cm.

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Answer 2

Step-by-step explanation:

A=96cm²

p Diagonal

16

cm

q Diagonal

12

cm

Solution

A=pq

2=16·12

2=96cm²