Work out the surface area of the prism.
To find the surface area, we have to add together the areas of all of the faces. Faces is another name for the sides. So here, this prism is made up of rectangles. So we need to find the area of each of these rectangles and add them together. And the area of a rectangle is equal to the length times the width. So we need to find the length and the width of each of these rectangles, multiply them together. And then, once we have each of these areas, we add them together. And this will give us the total surface area of the prism.
Let’s begin with the faces that we can see. Here, we have a five-by-three rectangle. And we don’t have any units, centimetres, metres, or anything like that. So we can just write units or 𝘶. So three units times five units would give us 15 units squared.
Now, let’s pick another face. At the top, we have a one-by-three rectangle. And we know that it’s a length of three because it’s parallel and exactly the same as this one here. So one times three would give us three. So we have three square units.
This next piece we’ll have to split up into rectangles because it’s not a rectangle. It’s rectangles put together. So it’s up to us how we wanna split this up. We can either split it here or split it here, either way. Let’s keep it here. So the one on the left would be a one by five, so five square units, and then the one on the right would be two by this length. Well, we would need to take four and then subtract one. So this would be a two-by-three rectangle, giving us six square units.
Now, we’ll have to begin working with the rectangles that we can’t really see. Let’s begin with this one. And it’s a three-by-three rectangle, making an area of nine square units. Now for this pink one, it would be a three by five minus two, so a three-by-three rectangle, making nine square units. Next, we’ll have an identical side as the one that we had to split up into two pieces, the one by five, so five square units, and the two by three, so six square units.
Next, we have this blue rectangle. That’s a two by three, so six units squared. And now finally, we have the bottom, which is four by three. So four times three gives us 12, so 12 square units. So now we have found the areas of all of the faces. So what’s left is to add them together. So we need to take 15 plus three plus five plus six plus nine plus nine plus five plus six plus six plus 12, giving us 76.
Therefore, the surface area of this prism would be 76 square units.