The total surface area of the shape is 215.8 in²
Explanation:
The shape can be divided into two parts
Area of rectangle 1 = 12 X 6
= 72 in²
Area of rectangle 2 = 8 X 6
= 48 in²
Area of rectangle 3 = 6 X 7
= 42 in²
Area of scalene triangle =
a = 7 in
b = 8 in
c = 12 in
[tex]S = \frac{a+b+c}{2} \\\\S = \frac{7+8+12}{2} \\\\S = 13.5[/tex]
[tex]A = \sqrt{S(S-a)(S-b)(S-c)} \\\\A = \sqrt{13.5(13.5 - 7)(13.5-8)(13.5-12)} \\\\A = \sqrt{13.5 X 6.5X5.5X1.5} \\\\A = 26.9[/tex]
Area of 2 scalene triangle = 26.9 X 2 in²
= 53.8 in²
Total surface area = 72 + 48 + 42 + 53.8 in²
= 215.8 in²
Therefore, total surface area of the shape is 215.8 in²
