Given the above composite figure, its surface area is evaluated to be the sum of the surface area of each of its plane surfaces.
Step 1:
Thus, the surface area of the figure:
[tex]=\text{area of ABCD + area of CDE + area of FGJ + area of GHIJ + area of BDGH + area of ACJI + area of EFDG + area of CEFJ + area of ABHI}[/tex]
The surface area of ABCD:
ABCD takes the shape of a rectangle. The area of a rectangle is given as
[tex]\text{length }\times\text{ width}[/tex]
Thus, the surface area of ABCD is calculated as
[tex]\text{Area}_{ABCD}\text{ = 8 cm }\times6cm=48cm^2[/tex]
The surface area of CDE:
CDE takes the shape of a triangle. The area of a triangle is given as
[tex]\frac{_{_{_{_{_{}}}}}1}{2}\times base\times height[/tex]
Thus, the surface area of CDE is calculated as
[tex]\text{Area}_{CDE}=\frac{1}{2}\times8\operatorname{cm}\text{ }\times3cm=12cm^2[/tex]
The surface area of FGJ:
FGJ has the same shape and dimension as CDE. Thus, the surface area of FGJ is 12cm²
The surface area of GHIJ:
GHIJ has the same shape and dimension as ABCD. Thus, the surface area of GHIJ is 48cm².
The surface area of BDGH:
BDGH takes the shape of a rectangle. Thus, its area will be
[tex]\text{Area}_{BDGH}=12\text{ cm }\times6cm=72cm^2[/tex]
The surface area of ACJI:
ACJI has the same shape and dimension as BDGH. Thus, its area will be 72 cm²
The surface area of CEFJ:
CEFJ has the shape of a rectangle. Its area will be calculated as
[tex]\begin{gathered} \text{Area}_{CEFJ}=\text{ 8cm }\times5\operatorname{cm} \\ =40\operatorname{cm}\text{ squared} \end{gathered}[/tex]
The surface area of EFGD:
Since EFGD has a similar shape and dimension as CEFJ, its area will as well be 40 cm²
The surface area of ABHI:
ABHI has the shape of a rectangle. Thus, its area will be
[tex]\text{Area}_{ABHI}=12\operatorname{cm}\times8\operatorname{cm}=96\operatorname{cm}\text{ squared}[/tex]
Step 2:
Sum the surface area of all plane surfaces of the composite figure
[tex]\begin{gathered} (48+12+12+48+72+72+40+40+96)cm^2 \\ =440\operatorname{cm}\text{ squared} \end{gathered}[/tex]
