Answer:
305 in^2
Step-by-step explanation:
First step is always to break up the problem into parts and write out our formulas- in this case, let's solve the easier part first, the bottom rectangular box type shape.
Area of a square or rectangle: A= length * height
Area of a triangle: A = 1/2 * length * height
Each side is 6x2, making each side 12 in^2, times four sides equals 48 in^2
The box also has a bottom, with dimensions of 6x6, equaling 36 in^2. be careful not to include the top, it may be included in this part of the problem that we're splitting up, but it's not in the actual figure.
Next up is the top portion- let's calculate the two triangular sides first. again, A=(1/2)l*h . so, these triangles are (1/2) * 5 * 4 , or 10 in^2 . With two triangular sides that's 20 in^2 total.
And now we only have two sides left, the rectangular parts of the triangular prism. They have a dimension of 5*6, equalling 30, and with two sides its a total of 60 in^2.
All of these sides can be added together:
48 + 36 + 20 + 60 = 305 in^2
