The given figure is composed of congruent isosceles right triangles. What is the area, in $\mathrm{cm}^{2}$, of the shaded part?
(a) 20
(d) 45
(b) 25
(e) 50
(c) 35

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-012.jpg?height=192&width=714&top_left_y=772&top_left_x=1119)
The correct option is (d).

Solution 1: The length of the hypotenuse of each of the five isosceles right triangles in the strip measures $30 \div 5=6 \mathrm{~cm}$. The square formed by four of these triangles has a side length of $6 \mathrm{~cm}$, so its area is $36 \mathrm{~cm}^{2}$. Therefore, each of the triangles has an area of $36 \div 4=9 \mathrm{~cm}^{2}$. Thus, the area of the shaded part measures $9 \times 5=45 \mathrm{~cm}^{2}$.

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-051.jpg?height=351&width=308&top_left_y=2200&top_left_x=1522)

Solution 2: The length of the hypotenuse of each of the five isosceles right triangles in the strip measures $30 \div 5=6 \mathrm{~cm}$. Denoting the legs of these triangles by $x$,
the Pythagorean Theorem provides $36=x^{2}+x^{2}=2 x^{2}$, that is, $x^{2}=18$, so the area of each of the five triangles in the strip measures $9 \mathrm{~cm}^{2}$. Thus, the area of the shaded part measures $5 \times 9=45 \mathrm{~cm}^{2}$.