Find the area of the blades of the magnetic compass shown in figure. (Take $\sqrt{11}= 3.32$).
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To do:

We have to find the area of the blades of the magnetic compass.

Solution:

Let $ABCD$ be a rhombus with each side $5\ cm$ and one diagonal $1\ cm$

Diagonal $BD$ divides into two equal triangles

Area of $\triangle ABD$,

$s=\frac{a+b+c}{2}$

$=\frac{5+5+1}{2}$

$=\frac{11}{2}$

Area of the triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{\frac{11}{2}(\frac{11}{2}-5)(\frac{11}{2}-5)(\frac{11}{2}-1)}$

$=\sqrt{\frac{11}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{9}{2}}$

$=\frac{3}{2 \times 2} \sqrt{11}$

$=\frac{3}{4} \sqrt{11} \mathrm{~cm}^{2}$

Total area of the rhombus $=2 \times \frac{3}{4} \sqrt{11}$

$=\frac{3}{2} \sqrt{11}$

$=1.5 \times 3.32$

$=4.98 \mathrm{~cm}^{2}$.

The area of the blades of the magnetic compass is $4.98\ cm^2$.

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Updated on: 10-Oct-2022

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