Prove that the two triangles shown below have the same area

In this picture the horizontal lines at the top and bottom are parallel. Prove that the yellow and red triangles are of the same area.

In this picture the horizontal lines at the top and bottom are parallel. Prove that the yellow and red triangles are of the same area.

Calculate the area of the triangle shown below.

In the picture below, the lines parallel to each side of the blue triangle through the opposite vertex are drawn to make the big triangle. How many triangles in the picture have the same area as that of the blue triangle? How many of them have the same measures of the blue triangle?

In the picture below, the lines parallel to each side of the blue triangle through the opposite vertex are drawn to make the big triangle. How many triangles in the picture have the same area as that of the blue triangle.

Prove that the two circles drawn on the two equal sides of an isosceles triangle as diameters pass through the mid point of the third side.

In the two pictures below, the squares are of the same size. Prove that the green regions are of the same area.

The coordinates of the vertices of a triangle are (3,5), (9,13), (10,6), Prove that this triangle is isosceles. Calculate its area.