Answer:
A = 25 units²
Step-by-step explanation:
First, figure out where the lines intersect.
Let's start with x = 0 and y = x:
because x = 0, substitute x in y = x
y = 0 so the intersection point of these two lines is (0,0)
With, x + y = 10 (or y = 10 - x) and x = 0:
substitute x again y = 10 - 0, so y = 10 and the intersection point is (0,10)
The last point has to be found by setting y = x and x + y = 10 (y = 10 - x) equal to each other: x = 10 - x
solve for x: x = 10 - x
2x = 10
x = 5
find y: y = 10 - 5
y = 5 and the intersection point is (5,5)
Now that you have the vertices of the triangle, you can find the area. (0,0) and (0,10) are on the y-axis and has a length of 10 units; this is your base. To find the height, you need to picture the triangle on the coordinate plane. Point (5,5) lines up with the midpoint (0,5) of the side with (0,0) and (0,10). From this, you can see that the height is 5 units.
Use the triangle area formula: A = 0.5bh
A = 0.5(10)(5)
= 0.5 × 50
A = 25 units²
