Question

The Total Surface Area for the shape below is _________.

Answer 1

The total surface area of the shape is 215.8 in²

Step-by-step 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

`S = (a+b+c)/(2) \\\\S = (7+8+12)/(2) \\\\S = 13.5`

`A = √(S(S-a)(S-b)(S-c)) \\\\A = √(13.5(13.5 - 7)(13.5-8)(13.5-12)) \\\\A = √(13.5 X 6.5X5.5X1.5) \\\\A = 26.9`

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