Question

A net of arectangular pyramidis shown. Therectangular base haslength 24 cm andwidth 21 cm. Thenet of the pyramidhas length 69.2 cmand width 64.6 cm.Find the surfacearea of the pyramid.

Answer 1

The Image will be of help

To find x

`\begin{gathered} x+24+x=69.2 \\ 2x+24=69.2 \\ 2x=69.2-24 \\ 2x=45.2 \\ x=(45.2)/(2) \\ x=22.6 \end{gathered}`

To find y

`\begin{gathered} y+21+y=64.6 \\ 2y+21=64.6 \\ 2y=64.6-21 \\ 2y=43.6 \\ y=(43.6)/(2) \\ y=21.8 \end{gathered}`

The diagram below will help us to find the Surface Area of the Pyramid

The surface area is

`SurfaceArea=A_1+2A_2+2A_3`

To find A1

`A_1=24*21=504`

To find A2

`\begin{gathered} A_2=(1)/(2)b* h \\ 2A_2=b* h \\ 2A_2=21*22.6 \\ 2A_2=474.6 \end{gathered}`

To find A3

`\begin{gathered} A_3=(1)/(2)bh \\ 2A_3=b* h \\ 2A_3=24*21.8 \\ 2A_3=523.2 \end{gathered}`

The surface Area

`\begin{gathered} SurfaceArea=A_1+2A_2+2A_3 \\ SurfaceArea=504+474.6+523.2 \\ SurfaceArea=1501.8cm^2 \end{gathered}`

Thus,

`SurfaceArea=1501.8cm^2`