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Find the Area of the Following Regular Hexagon. - Mathematics

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ConceptArea of a Polygon

Question

Find the area of the following regular hexagon.

Solution

The given figure is:
Join QN.

It is given that the hexagon is regular. So, all its sides must be equal to 13 cm.
Also, AN = BQ
QB+BA+AN = QN
AN+13+AN = 23
2AN = 23-13 = 10
\[AN =\frac{10}{2}= 5 cm\]
Hence, AN = BQ = 5 cm
Now, in the right angle triangle MAN:
\[ {MN}^2 {=AN}^2 {+AM}^2 \]
\[ {13}^2 {=5}^2 {+AM}^2 \]
\[ {AM}^2 =169-25=144\]
\[AM=\sqrt{144}=12cm.\]
\[\therefore OM = RP = 2\times AM = 2\times12 = 24 cm\]
Hence, area of the regular hexagon = (area of triangle MON)+(area of rectangle MOPR)+(area of triangle RPQ)
\[=(\frac{1}{2}\times OM\times AN)+(RP\times PO)+(\frac{1}{2}\times RP\times BQ)\]
\[=(\frac{1}{2}\times24\times5)+(24\times13)+(\frac{1}{2}\times24\times5)\]
\[=60+312+60\]
\[ {=432 cm}^2\]
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APPEARS IN

 RD Sharma Solution for Mathematics for Class 8 by R D Sharma (2019-2020 Session) (2017 to Current)
Chapter 20: Mensuration - I (Area of a Trapezium and a Polygon)
Ex. 20.3 | Q: 5 | Page no. 29
Solution Find the Area of the Following Regular Hexagon. Concept: Area of a Polygon.
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