Question

11. The length of a side of a rhombus is 4.1 cm and one of its diagonals is 1.8cm.
Find the area of the rhombus
(2011
(1) 10.8 sq cm (2) 3.5 sq cm (3) 7.2 sqcm 141 8.1 cm​

Answer 1

Answer:

7.2cm²

Step-by-step explanation:

Given: the length of a side is 4.1cm

Diagonal is 1.8cm.

To Find: Area of the rhombus.

Procedure:

$\bf Area \ of \ rhombus = \dfrac{D1 \times D2}{2}$

$\sf \implies Area \ of \ rhombus= \dfrac{1}{2} \times 1.8 \sqrt{4(4.1)^2 - 1.8^2}$

$\implies \sf Area \ of \ rhombus = \dfrac{1}{2} \times 1.8 \sqrt{4(16.81) - (3.24)}$

$\implies \sf Area \ of \ rhombus = \dfrac{1}{2} \times 1.8 \sqrt{(67.24) - (3.24)}$

$\implies \sf Area \ of \ rhombus = \dfrac{1}{2} \times 1.8 \sqrt{64}$

$\implies \sf Area \ of \ rhombus = \dfrac{1}{2} \times 1.8 \times 8$

$\implies \sf Area \ of \ rhombus = 1.8 \times 4$

$\sf \implies Area \ of \ rhombus = 7.2cm^2$

• A rhombus is a quadrilateral, where the diagonals intersect at 90°.

• The opposite angles of a rhombus are equaareto each other.

• All 4sides of a rhombus is equal.

• Opposite sides of a parallelogram are equal.

Answer 2

Given:-

• Length of a side of a rhombus is 4.1 cm.
• It's diagonal is 1.8 cm.

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To find:-

• Area of the rhombus.

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Solution:-

Here,

• Side = 4.1 cm
• Diagonal = 1.8 cm

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★Formula used:-

${\dag}\:{\underline{\boxed{\sf{\purple{Area\: of\: rhombus = \dfrac{1}{2} \times D_1 \times D_2}}}}}$

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$\tt\longmapsto{A = \dfrac{1}{2} \times D_1 \sqrt{4s^2 - {D_1}^2}}$

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$\tt\longmapsto{A = \dfrac{1}{2} \times 1.8 \sqrt{4(4.1)^2 - 1.8^2}}$

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$\sf\longmapsto{\boxed{\orange{A = 7.2\: cm^2}}}$

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Hence,

• the area of the rhombus is 7.2 cm².

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Therefore,

• Option (3) is correct.

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★More to know :-

$\sf{Area\;of\;Rectangle\;=\;Length\;\times\;Breadth}$

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$\sf{Area\;of\;Square\;=\;(Side)^{2}}$

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$\sf{Area\;of\;Triangle\;=\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

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$\sf{Area\;of\;Parallelogram\;=\;Base\;\times\;Height}$

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$\sf{Area\;of\;Circle\;=\;\pi r^{2}}$

$\sf{Perimeter\;of\;Rectangle\;=\;2\;\times\;(Length\;+\;Breadth)}$

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$\sf{Perimeter\;of\;Rectangle\;=\;4\;\times\;(Side)}$

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$\sf{Perimeter\;of\;Circle\;=\;2\pi r}$