You want to find the surface area. We can do this by finding the area of each side and combining together.
1. We have two sides that are triangles. The surface area of a triangle is A
A = 1/2 bh
A = area
b = length of base = 3
h = length of height = 4
Thus, the surface area of the two triangles are
A = 1/2 (2)(4) = 1/2(8) = 4 cm^2
2. Now, lets find the surface area of the bottom of the figure. This is a square so the formula for area is
A = LW
A = area
L = length of rectangle = 5
W = width of rectangle = 3
Thus,
A = LW = 5 * 3 = 15 cm^2
Therefore, the surface area of the bottom is 15 cm^2.
3. Now, lets find the side that is furthest to the right. This is again a rectangle so the formula for area is
A = LW
A = area
L = length of rectangle = 5
W = width of rectangle = 4
Thus,
A = LW = 5 * 4 = 20 cm^2
Therefore, the surface area of the side is 20 cm^2.
4. Finally, lets find the surface area of the slanted side. This is once again a rectangle. Therefore, the formula for area is
A = LW
A = area
L = length of rectangle = 5
W = width of rectangle = 5
Thus,
A = LW = 5 * 5 = 25 cm^2
Therefore, the surface area of the slanted side is 25 cm^2.
Now, lets add all of the areas up.
Triangle 1 = 4 cm^2
Triangle 2 = 4 cm^2
Bottom Rectangle = 15 cm^2
Right Side Rectangle = 20 cm^2
Slanted Side Rectangle = 25 cm^2
Total Surface Area = 68 cm^2