Question

SURFACE AREAS - PYRAMIDS?

Answer 1

The total surface area consists of the base area and the surface area (the area of all lateral faces). The base is a hexagon with side a=3 cm.

`A_(hexagon)=6A_(triangle)=6\cdot (1)/(2) \cdot (a^2√(3))/(4) =(3)/(4) \cdot 3^2\cdot √(3)=(27√(3))/(4)` sq. cm.

Each lateral face is an isosceles triangle with height h=12 cm and base a=3 cm. The area of one such lateral triangle is

`A_(lateral)=(1)/(2)\cdot h\cdot a= (1)/(2)\cdot 12\cdot 3=18` sq. cm.

Then the total surface area is:

`A_(total)= (27√(3))/(4) +6\cdot 18=(27√(3))/(4) +108=11.7+108=119.7` sq. cm.

Answer: 119.7 sq. cm.