Solution
The Image will be of help
To find x
[tex]\begin{gathered} x+24+x=69.2 \\ 2x+24=69.2 \\ 2x=69.2-24 \\ 2x=45.2 \\ x=\frac{45.2}{2} \\ x=22.6 \end{gathered}[/tex]
To find y
[tex]\begin{gathered} y+21+y=64.6 \\ 2y+21=64.6 \\ 2y=64.6-21 \\ 2y=43.6 \\ y=\frac{43.6}{2} \\ y=21.8 \end{gathered}[/tex]
The diagram below will help us to find the Surface Area of the Pyramid
The surface area is
[tex]SurfaceArea=A_1+2A_2+2A_3[/tex]
To find A1
[tex]A_1=24\times21=504[/tex]
To find A2
[tex]\begin{gathered} A_2=\frac{1}{2}b\times h \\ 2A_2=b\times h \\ 2A_2=21\times22.6 \\ 2A_2=474.6 \end{gathered}[/tex]
To find A3
[tex]\begin{gathered} A_3=\frac{1}{2}bh \\ 2A_3=b\times h \\ 2A_3=24\times21.8 \\ 2A_3=523.2 \end{gathered}[/tex]
The surface Area
[tex]\begin{gathered} SurfaceArea=A_1+2A_2+2A_3 \\ SurfaceArea=504+474.6+523.2 \\ SurfaceArea=1501.8cm^2 \end{gathered}[/tex]
Thus,
[tex]SurfaceArea=1501.8cm^2[/tex]
