If you make 2 more triangles with the diagram, maybe that will help:

you can notice that a side made from P and Q are is a side to another right triangle made by the x and y axis themselves.

the height of this right triangle is 3 (from (0,0) to (0,3))
the base of this right triangle is 4 (from (0,0) to (4,0))

the hypotenuse is 5 which means that side PQ is 5.

Side PR also has a length of 5 b/c you can make a right triangle with base of 3 (from 4,0 to 7,0) and height of 4 (from 7,0 to 7,4)

now we know this is a 45 -45-90

both base and height is 5

so (1/2)(5*5) = 25/2 = 12.5

(A)

if you take the length of the sides of the triangle, it is 5,5,5sqrt(2)
clearly a 45-45-90 triangle

area is (1/2)*5*5
12.5

Its just the area of the trapezium - area of the two triangles..

i.e. 1/2(3+4)*7 - 12 = 12.5

This is very easy if you know how to represent it in the matrix format

Cant you take the area of a square which is 28 units and subtract the value of the negative space 15.5 around the central triangle for a value of 12.5?

artistocrat wrote:Can't you simply draw a box around the triangle and divide the area of the box by 2. Furthest x coordinate is 7 times greatest y coordinate is 4 equals 28. 28/2=14?

and how can you be sure that the area of the triangle is half the area of the box

Right.