Answer:
620 cm²
Step-by-step explanation:
First I'll describe the net. There are 3 rectangles and 2 triangles. The triangles are identical and 2 out 3 of the rectangles are the same.
So, we know that the two similar rectangles have measurements of 13cm x 10cm. So, that's 130 cm² for one such rectangle. Add the other one and we get 260 cm².
The bottom rectangle has dimensions of 10cm x 24 cm, or 240 cm². Add that to our previous total and we'll get 500 cm².
On to the triangles. Now, we know that 1. these are isosceles triangles, and 2. they have a height of 5 cm. We can pretend to cut them in half at their highest point, which would give us 4 triangles with height 5 and length 12. Now, if you put two identical triangles together, it's a four-sided shape, and you can just multiply length by width. Let's do that.
Now we have 2 rectangles, each with width 5 and length 12. Calculate the area for each, and now we have 2 rectangles with area 60 cm². Add them together....120cm².
Add that to our previous total, and we'll get 620 cm². That should be the surface area of your prism :D
