Sainik School Entrance Exam 2021 Solved Paper

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Question : 24 of 150

Marks: +1, -0

Find the area of a rhombus having perimeter

80 {\cm}

and one diagonal

24 {\cm}

.

$354 \sq. {\cm}$ .
$364 \sq. {\cm}$ .
$384 \sq. \cm.$
$480 \sq. {\cm}$ .

Solution:

(c) Perimeter of rhombus

=80 {\cm}

∴ Side of rhombus

={80}/{4}=20 {\cm}

.

One diagonal

(B D)

of rhombus is

24 {\cm}

.

∴ B O={24}/{2}=12 {\cm}

In

△ A O B

,

A O^2=A B^2-O B^2=20^2-12^2=400-144

∴ A O^2=256 ⇒A O=√{256}=16 {\cm}

∴

Other diagonal

A C=2 ×A O=2 × 16=32 {\cm}

.
Area of rhombus

={1}/{2} ×d_1 ×d_2={1}/{2} ×24 832=384 { \sq. } {\cm} .

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