The answer is false because if you attach to triangles together in a way so that the figure would have 4 straight lines, you will get a rectangle. that means half of a rectangle is a triangle, so the area of both cannot be the same even if they have the same base and height.
for example the base and height of both is 3cm and 5cm.
area of the rectangle then would be, area= base× height =3cm×5cm=15cmsquared
then the area of the triangle would be, area= base×height divided by 2 =3cm×5cm÷2= 7.5cm
