What is the area of the triangle on the front of Keith’s math folder?
Well, in the diagram, this is the triangle we’re talking about. Now assuming that Keith’s math folder is in the shape of a rectangle, that will make the angle in all of those corners 90 degrees, and it would make opposite sides equal in length. So this dimension here would also be one foot. And the question also gives us the fact that this distance here, which is perpendicular to the base or to this side of the triangle, is 10 inches.
Now you should recall that the area of a triangle is equal to half times the length of its base times its perpendicular height. Now I’m gonna redraw the triangles. I’m gonna turn it round in 90 degrees in that direction, and let’s see what it looks like. And in this orientation, it’s fairly easy to see that the base here is one foot and the perpendicular height, which is the height which is at 90 degrees to the base, is 10 inches. So I can go ahead and calculate the area of this triangle.
But before we do that, we should take the time to notice that this dimension here is in inches, and this dimension here is in feet. They’re different units. We need to have the same unit in order to do the calculation. Now I would suggest that the easiest one to change is feet. One foot is 12 inches. So instead of writing on foot, I’m gonna write 12 inches.
Okay. We can now substitute these numbers into our formula. So the area is a half times the base, is 12, and the perpendicular height was 10. And a half times 12 is six, and six times 10 is 60. So the area is 60, and area is in square units. Our length units were inches, so the area unit is gonna be square inches. And there we have it. The answer is: The area is 60 square inches.