Find the lateral area and the surface area of the regular hexagonal pyramid.Question 8 options:lateral area = 385.1 cm2; surface area = 805 cm2lateral area = 231.6 cm2; surface area = 441 cm2lateral area = 210 cm2; surface area = 325.5 cm2lateral area = 21.8 cm2; surface area = 231.2 cm2

Answer:Part 1) The lateral area is [tex]LA=210\ cm^2[/tex]Part 2) The surface area is [tex]SA=325.5\ cm^2[/tex]solateral area = 210 cm2; surface area = 325.5 cm2Step-by-step explanation:Part 1) Find the lateral area of the regular hexagonal pyramidThe lateral area is equal to the area of its six triangular facesso[tex]LA=6[\frac{1}{2}bh][/tex]we have[tex]b=7\ cm\\h=10\ cm[/tex]substitute[tex]LA=6[\frac{1}{2}(7)(10)][/tex][tex]LA=210\ cm^2[/tex]Part 2) Find the surface area of the regular hexagonal pyramidThe surface area is equal to the lateral area plus the area of the hexagonal baseso[tex]SA=LA+B[/tex]whereB is the area of the hexagonal baseFind the area of the hexagonal baseThe area of the regular hexagon is equal to the area of six equilateral triangles[tex]B=6[\frac{1}{2}(b)(h)][/tex]we have[tex]b=7\ cm\\h=5.5\ cm[/tex]substitute[tex]B=6[\frac{1}{2}(7)(5.5)][/tex][tex]B=115.5\ cm^2[/tex]The surface area is equal to[tex]SA=210+115.5=325.5\ cm^2[/tex]