Answer:
[tex]SA=578\text{ mm}^2[/tex]
Step-by-step explanation:
We can find the total surface area of the figure by adding the areas of each of its sides:
[tex]SA = 2( A_\triangle) + 2(A_{\square1}) + A_{\square2}[/tex]
Plugging in the sides' respective area formulas, we get:
[tex]SA = 2(\frac{1}{2}bh) + 2(l_1w_1) + 2(l_2w_2)[/tex]
We can define the following variable values based on the given drawing:
- [tex]b=10.2[/tex]
- [tex]h=6[/tex]
- [tex]l_1 = 19[/tex]
- [tex]w_1=8.5[/tex]
- [tex]l_2=19[/tex]
- [tex]w_2=10.2[/tex]
Plugging these numerical values into the surface area equation, we get:
[tex]SA = 2(\frac{1}{2})(10.2)(6) + 2(19)(8.5) + 2(19)(10.2)[/tex]
Evaluating the expression on the right side, we get:
[tex]\boxed{SA=578\text{ mm}^2}[/tex]
