Answer:
290 cm²
Step-by-step explanation:
Area of regular hexagon-based pyramid.
First find the area of 6 triangles and then the area of the regular hexagon.
Slant height = s = 15 cm
side = b = 5 cm
[tex]\sf Area \ of \ triangle = \dfrac{1}{2}*b* s\\\\Area \ of \ 6 \ triangle = 6*\dfrac{1}{2}*b*s\\\\[/tex]
= 3 bs
= 3 * 5 * 15
= 225 cm²
[tex]\sf Area \ of \ regular \ hexagon = \dfrac{3\sqrt{3}b^2}{2}\\\\[/tex]
[tex]\sf =\dfrac{3*1.732*5*5}{2}\\\\= 64.95 \ cm^2[/tex]
Area of regular hexagon based polygon = Area of 6 triangles + area of regular hexagon
= 225 + 64.95
= 289.95
= 290.0 cm²
