Question

What is the surface area of the regular pyramid below?1212

Answer 1

`Surface\text{ area of the regular pyramid = 648 sq units \lparen option A\rparen}`

Step-by-step explanation:

Given:

The dimension of the base of the pyramid: 12 by 12

The slant height = 21

To find:

the surface area of the pyramid

To determine the surface area, we will apply the formula:

`Surface\text{ area = Area + }(1)/(2)(perimeter)(slant\text{ height\rparen}`
`\begin{gathered} The\text{ base is a square. } \\ \text{Area of the base = Area of the square} \\ \\ Area\text{ of the base = side}^2 \\ Area\text{ of the base = 12}^2\text{ = 144} \end{gathered}`
`\begin{gathered} Perimeter\text{ of the base = 4\lparen side\rparen} \\ Perimeter\text{ of the base = 4\lparen12\rparen} \\ \\ \text{ Perimeter of the base = 48} \end{gathered}`
`\begin{gathered} Surface\text{ area of the regular pyramid = }144\text{ + }(1)/(2)(48*21) \\ \\ Surface\text{ area of the regular pyramid = 648 sq units \lparen option A\rparen} \end{gathered}`