Chapter 12.7, Problem 1GP

To determine

The lateral and surface area of the square pyramid is to be estimated:

Length of base: $6cm$

Slant height: $18.4cm$

Answer to Problem 1GP

The lateral and surface area of the square pyramid is $223.71c{m}^2,259.71c{m}^2$ respectively.

Explanation of Solution

Given:

  $\begin{array}{l}a=6cm\\ h=18.4cm\end{array}$

Concept Used:

The lateral surface area of the square pyramid is given by the following expression:

  $L=a\sqrt{a^2+4h^2}$

The surface area of the square pyramid is given by the following expression:

  $A=a^2+a\sqrt{a^2+4h^2}$

Calculation:

The lateral surface area of the square pyramid is calculated as:

  $\begin{array}{l}L=a\sqrt{a^2+4h^2}\\ L=6\sqrt{{\left(6\right)}^2+4{\left(18.4\right)}^2}\\ L=223.71c{m}^2\end{array}$

The surface area of the square pyramid is calculated as:

  $\begin{array}{l}A=a^2+a\sqrt{a^2+4h^2}\\ A={\left(6\right)}^2+223.71\\ A=259.71c{m}^2\end{array}$

Conclusion:

Hence, the lateral and surface area of the square pyramid are calculated as above.