Solve the problem. Find the surface area of a right regular hexagonal pyramid with sides 2 cm and slant height 5 cm. Round youranswer to the nearest hundredth.
Accepted Solution
A:
Answer:The surface area of the right regular hexagonal pyramid is 50.78 cm².Step-by-step explanation:Given:A right regular hexagonal pyramid with sides(s) 2 cm and slant height(h) 5 cm.Now, to find the surface area(SA) of the right regular hexagonal pyramid.So, we find the area of the base(b) first:Area of the base = [tex]\sqrt[3]{3}\times s^{2}[/tex] = [tex]\sqrt[3]{3}\times 2^{2}[/tex]On solving we get:Area of the base(b) = [tex]20.784[/tex]Then, we find the perimeter(p) :Perimeter = s × 6[tex]p=2\times 6=12[/tex]Now, putting the formula for getting the surface area:Surface area = perimeter × height/2 + Area of the base.[tex]SA=\frac{p\times h}{2}+b[/tex][tex]SA=\frac{12\times 5}{2}+20.784[/tex][tex]SA=30+20.784[/tex][tex]SA=50.784[/tex]As, the surface area is 50.784 and rounding to nearest hundredth becomes 50.78 because in hundredth place it is 8 and in thousandth place it is 4 so rounding to it become 50.78.Therefore, the surface area of the right regular hexagonal pyramid is 50.78 cm².