Question

Jeremy cut a rhombus out of a 10-inch rectangle. The diagonals of the rhombus are parallel and perpendicular to the sides of the rectangle and are congruent to the length and width of the rectangle, respectively. What is the total area of the four shaded triangles?

Answer 1

The total area of the four shaded right triangles that make up the rhombus in the right is 1/2 of the area of the rectangle:

$$A_t=\frac12a·h_a=\frac12 a·\frac b2=\frac{ab}4.$$

Two such triangles are

$$A=2A_t=\frac {ab}2.$$