93.382 square cm
Work Shown:
The green triangle in the back has height 2.6 and an unknown base x. Half of this is x/2, which I'll call y. So y = x/2.
The green triangle in the back is split along the vertical dotted line to get two right triangles. The base of each right triangle is y = x/2.
Use the Pythagorean theorem to find y. Use that to find x
a^2+b^2 = c^2
y^2+(2.6)^2 = (3.2)^2
y^2 + 6.76 = 10.24
y^2 = 10.24 - 6.76
y^2 = 3.48
y = sqrt(3.48) apply square root
y = 1.8654758 approximately
x/2 = 1.8654758
x = 2*1.8654758
x = 3.7309516 also approximate
The base of the triangle is roughly 3.7309516 meters
We can now find the area of one green triangle
area of triangle = base*height/2 = 3.7309516*2.6/2 = 4.85023708
two triangles have approximate area 2*(4.85023708) = 9.70047416
So far we've only considered the triangular faces. There are 3 more faces which are the rectangular sides. These are known as the lateral sides.
One way to get the lateral surface area is to multiply the perimeter of the triangle by the depth of the prism
perimeter of triangle = (side1)+(side2)+(side3)
perimeter = 3.7309516 + 3.2 + 3.2
perimeter = 10.1309516
lateral surface area = (depth)*(perimeter)
lateral surface area = (8.26)*(10.1309516)
lateral surface area = 83.681660216
The last step is to add this lateral surface area onto the area of the two triangles to get the full surface area
surface area = (triangular area) + (lateral surface area)
surface area = (9.70047416) + (83.681660216)
surface area = 93.382134376
surface area = 93.382 square cm
