Question

Using the figure, calculate the total surface area of the pyramid.

Answer 1

Given:

There is a figure given in the question

Required:

We need to find the surface area of given figure of pyramid

Step-by-step explanation:

First we need to find the side of base square

use tan function

`\begin{gathered} \tan30=(SM)/(DM) \\ \\ (1)/(√(3))=(6)/(DM) \\ \\ DM=6√(3) \end{gathered}`

now to find the side of base square is

`DC=2DM=12√(3)`

The surface area of pyramid is

`TSA=(1)/(2)Pl+B`

where P is base of perimeter

l is the slant height which is 6 cm

B is the base area

now find P

`P=4*12√(3)=48√(3)\text{ cm}`

now find B

`B=12√(3)*12√(3)=432\text{ cm}^2`

now substitute all the values in the formula of Total surface area of pyramid

`TSA=(1)/(2)Pl+B=(1)/(2)*48√(3)*6+432`

simplify as:

`\begin{gathered} =249.4+432 \\ =681.4\text{ cm}^2 \end{gathered}`

Final answer:

Total surface area of given figure is 681.4 square cm