Find the area of the following regular hexagon

1.	Find the area of the following regular hexagon
Answer» NQ = 23 cm given ND + QC = 23 -13 = 10 ND = QC = 5 cm OM = 24 cm Area of given hexagon = 2 times area of triangle MNO + area of rectangle MOPR Area of right angled triangle = \(\frac{1}{2}\)x base x altitude Area of rectangle = length × breadth Area of regular hexagon = \(\frac{1}{2}\)x OM x ND + MO x OP + \(\frac{1}{2}\) x RP x QC Area of given hexagon = \(\frac{1}{2}\) x 24 x 5 + 24 x 13 + \(\frac{1}{2}\) x 24 x 5 = 432 cm² Therefore area of given hexagon is 432 cm²

Answer»

NQ = 23 cm given

ND + QC = 23 -13 = 10

ND = QC = 5 cm

OM = 24 cm

Area of given hexagon = 2 times area of triangle MNO + area of rectangle MOPR

Area of right angled triangle = \(\frac{1}{2}\)x base x altitude

Area of rectangle = length × breadth

Area of regular hexagon = \(\frac{1}{2}\)x OM x ND + MO x OP + \(\frac{1}{2}\) x RP x QC

Area of given hexagon = \(\frac{1}{2}\) x 24 x 5 + 24 x 13 + \(\frac{1}{2}\) x 24 x 5 = 432 cm²

Therefore area of given hexagon is 432 cm²

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