Chapter 12, Problem 7CR

To determine

To find:The area of base, lateral area, and slant height of a regular square pyramid.

Answer to Problem 7CR

The area of base, lateral area, and slant height are 900, 1020 and 17 respectively.

Explanation of Solution

Given information:

A regular square pyramid has base edge 30 and total area is 1920.

Formula used: The formula to find the lateral area of a pyramid is:

  $\text{Lateral area}=\frac{1}{2}\times \text{perimeter}\times \text{slant}\text{height}$

Calculation:

The given pyramid is a square pyramid. So, the shape of the base of pyramid is square.

The edge of the base is 30. So, the area of the base can be calculated as:

  $\begin{array}{c}\text{area of base}=\text{ side}\times \text{side}\\ =30\times 30\\ =900\end{array}$

Now, lateral area of the pyramid can be calculated as:

  $\begin{array}{c}\text{lateral area }=\text{ Total area}-\text{base area}\\ =1920-900\\ =1020\end{array}$

The slant height is calculated as:

  $\begin{array}{c}\text{lateral area = }\frac{1}{2}\times \text{perimeter}\times \text{slant height}\\ 1020=\frac{1}{2}\times \left(4\times 30\right)\times \text{slant height}\\ \text{slant height = }\frac{1020}{60}\\ =17\end{array}$

Therefore, the area of base, lateral area, and slant height of the square pyramid are 900, 1020 and 17 respectively.