Answer:
To find the area of the polygon with the given vertices A(-5, 0), B(0, 10), and C(15, 0), you can use the formula for the area of a triangle when you have the coordinates of its vertices. The formula is:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
In this case, A(-5, 0), B(0, 10), and C(15, 0), so you can plug in these coordinates into the formula:
Area = 1/2 * |-5(10 - 0) + 0(0 - 0) + 15(0 - 10)|
Simplify the expression inside the absolute value:
Area = 1/2 * |-50 + 0 - 150|
Now, continue simplifying:
Area = 1/2 * |-200|
Since we're taking the absolute value, it becomes:
Area = 1/2 * 200
Now, calculate the area:
Area = 100 square units
So, the area of the polygon is 100 square units.
You can also use the distance formula, but this way is faster to me :-p