Answer:
A = 62.5
Step-by-step explanation:
I would break this up into two easier cases. the square at the top where three vertices are A,B, and C. and then the triangle for the rest of the area. we can use the distance formula to find the side length of the square.
sqrt((y2-y1)^2 + (x2-x1)^2)
sqrt((5-2)^2 + (-1-3)^2)
sqrt(3^2 + (-4)^2)
sqrt(9 + 16)
sqrt ( 25)
5
so the area of the square is 5^2 =25
now for the triangle. the formula for the area of a triangle is (1/2)bh.
so we can plug in our b=5, but we need to find h.
we use the distance formula between point A and D to find the distance to be 20, but we have to subtract the 5 we already counted in the area of the square. so the height is 15.
so The triangle has area (1/2)×5×15
37.5.
add the two areas together and we get our answer
25+37.5 = 62.5
