Answer:
390 [tex]in^{2}[/tex]
Step-by-step explanation:
We know that the top is a rectangle triangle, we only have two of the tree sides and the one that is missing is the hypotenuse. The formula to find it is [tex]h^{2}= a^{2} +b^{2}[/tex]
If we put the values we know it would be
[tex]h^{2}= 5^{2} +12^{2}[/tex]
[tex]h^{2}= 25 +144[/tex]
[tex]h^{2}= 169[/tex]
[tex]h=\sqrt{169}[/tex] = 13
So now we have the lenght missing.
The area of the top and bottom is the same and we found it by the formula [tex]\frac{(base)(height)}{2}[/tex] = [tex]\frac{(12)(5)}{2}[/tex] = 30, that is the area of just one triangle, multiply by 2 and that is the area of top and bottom = 30 x 2 = 60
The area of a rectangle is base x height, we have three rectangles.
First one: 13 x 11 = 143
Second one: 5 x 11 = 55
Third one: 12 x 11 = 132
The sum of the areas would be = 60 + 143 + 55 + 132 = 390 [tex]in^{2}[/tex]
