A right pyramid with a regular hexagon base has a height of 3 units

A right pyramid with a regular hexagon base has a height of 3 units If a side of the hexagon is 6 units long, then the apothem is 3 units long The slant height is the hypotenuse of a right triangle formed with the apothem and the Using the Pythagorean theorem c- + b2 to find the slant height results in a slant height of units The lateral area issquare units

Part a) The slant height is Part b) The lateral area is equal to Step-by-step explanation:we know thatThe lateral area of a right pyramid with a regular hexagon base is equal to the area of its six triangular facessowhereb is the length side of the hexagonl is the slant height of the pyramidPart a) Find the slant height lApplying the Pythagoras Theoremwhereh is the height of the pyramida is the apothemwe havesubstitutePart b) Find the lateral areawe havesubstitute the values

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< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

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