Chapter 12, Problem 18SGR

To determine

To find the lateral and surface area of the given pyramid.

Answer to Problem 18SGR

Lateral surface $=72$ square meters

Surface area $=81$ square meters

Explanation of Solution

Given:

  

A square pyramid

Slant height of the pyramid, $(l)$

  $=6$ meters

Side of the square base, $(a)$

  $=3$ meters

Formula used:

Lateral surface area of a pyramid $=$

  $pl$

where $p$ is the perimeter of the base of the pyramid, and $l$ is the slant height of the pyramid.

Total surface area of a pyramid $=pl+B$

where $p$ is the perimeter of the base , $l$ is the slant height of the pyramid and $B$ is the base area of he pyramid.

Perimeter of a square $=4\times a$

where a is the side of the square.

Area of a square $=a^2$

where a is the side of the square.

Calculation:

To find the lateral surface area of the pyramid, use the following formula.

Lateral surface area $=pl$

  $\Rightarrow (4\times a)\times l$

Now putting the values,

  $\Rightarrow (4\times 3)\times 6$

  $\Rightarrow 72$ square meters

So, the lateral surface area of the pyramid is 72 square meters.

To find the surface area of the pyramid, use the following formula.

Lateral surface area $=pl\times B$

  $\Rightarrow \left(4\times a\right)\times l+(a^2)$

Now putting the values,

  $\Rightarrow (4\times 3)\times 6+(3^2)$

  $\Rightarrow 81$ square meters

So, the surface area of the pyramid is 81 square meters.

Conclusion:

Hence, the lateral surface area is 72 square meters and surface area is 81 square meters.