Question

find the area of a rhombus having each side equal to 13 cm and one of whose diagonals is 10 cm......​

Answer 1

Answer:

60

Step-by-step explanation:

Answer 2

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

Given :

• Eαch side of α rhombus = 13cm.
• One of the diαgonαl = 10cm.

To Find :

• Areα of the rhombus.

Knowledge Required :

Pythαgorαs theorem —

$\large\star{\boxed{\sf{\purple{ (Base)^{2}+(Perpendicular)^{2} = (Hypotenuse)^{2}}}}}$

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$\large\star{\boxed{\sf{\purple{ Area_{(rhombus)}= \dfrac{1}{2} \times d_{1} \times d_{2}}}}}$

Step by step Explαnαtion :

:$\implies{\sf{ (OA)^{2} + (OB)^{2} = (AB)^{2}}}$

:$\implies{\sf{ (OA)^{2} + (\dfrac{10}{2})^{2} = (13)^{2}}}$

:$\implies{\sf{ (OA)^{2} + (5)^{2} = (13)^{2}}}$

:$\implies{\sf{ (OA)^{2} + 25 = 169}}$

:$\implies{\sf{(OA)^{2}= 169-25}}$

:$\implies{\sf{ (OA)=144}}$

:$\implies{\sf{ OA = \sqrt{144}}}$

:$\implies{\sf{ OA = 12}}$

Now,

$\displaystyle{\sf{ AC = OA \times 2}}$

$\implies{\sf{ AC = 12\times 2}}$

$\implies{\sf{ AC = 24cm}}$

After thαt,

• Substitute the vαlues in the formulαe of αreα of rhombus.

$\longrightarrow{\sf{ \dfrac{1}{2} \times 24cm \times 10cm}}$

$\longrightarrow{\sf{ \dfrac{1}{\cancel{2}} \times \cancel{24cm} \times 10cm}}$

$\longrightarrow{\sf{ 12cm \times 10cm}}$

$\implies{\boxed{\sf{\purple{ 120cm^{2}}}}}$

Hence, the αreα of rhombus is 120cm².

And we αre done! :D

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