Chapter 12.3, Problem 3ACYP

To determine

Tofind:The surface area of the given pyramid.

Answer to Problem 3ACYP

The surface area of the given pyramid is $100$ ft².

Explanation of Solution

Given information:

The pyramid is shown in Figure-1 here

Formulaused:

The surface area of pyramid is given by $S=\frac{1}{2}Pl+B$ , where P the perimeter of the base, l the slant height, and B the area of the base.

Calculations:

The base of the given pyramid is a right angle isosceles triangle with each equal side 6 ft. Therefore, the third side of the base triangle is of length $6\sqrt{2}$ ft.

The perimeter of the base of pyramid is $P=6+6+6\sqrt{2}=12+8.5=20.5$ ft and area of the base $B=\frac{1}{2}6\times 6=18$ ft².

The slant height of the pyramid is 8 ft.

Hence, the surface area of the given pyramid is $S=\frac{1}{2}\left(20.5\right)\times 8+18=100$ ft².

Conclusion:

The surface area of the given pyramid is $100$ ft².