Chapter 12.3, Problem 3BCYP

To determine

Tofind:The surface area of the given pyramid.

Answer to Problem 3BCYP

The surface area of the given pyramid is 97.5 inch².

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 pentagon with each equal side 4 inches.

The perimeter of the base of pyramid is $P=5\times 4=20$ inches.

The area of the pentagon with each side p unit is given by $A=1.72\times p^2$ .

Here, $p=4$ , therefore, $A=1.72\times {\left(4\right)}^2=27.53$ inch²

Thus, he area of the base of pyramid is $B=27.53$ inch².

The slant height of the pyramid is 7inches.

Hence, the surface area of the given pyramid is $S=\frac{1}{2}20\times 7+27.53=97.53$ inch².

Conclusion:

The surface area of the given pyramid is 97.5 inch².