The diagram shows two isosceles right-triangles with sides as marked. What is the area of the shaded region?
(A) $4.5 \mathrm{~cm}^{2}$
(B) $8 \mathrm{~cm}^{2}$
(C) $12.5 \mathrm{~cm}^{2}$
(D) $16 \mathrm{~cm}^{2}$
(E) $17 \mathrm{~cm}^{2}$

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-097.jpg?height=236&width=458&top_left_y=2121&top_left_x=1300)
The diagram shows two isosceles right-triangles with sides as marked. What is the area of the shaded region?
(A) $4.5 \mathrm{~cm}^{2}$
(B) $8 \mathrm{~cm}^{2}$
(C) $12.5 \mathrm{~cm}^{2}$
(D) $16 \mathrm{~cm}^{2}$
(E) $17 \mathrm{~cm}^{2}$

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-422.jpg?height=230&width=442&top_left_y=877&top_left_x=1297)

## Solution

The area of the larger triangle is $\frac{1}{2}(5)(5)$.

The area of the smaller triangle is $\frac{1}{2}(3)(3)$.

The shaded area is, $\frac{1}{2}(5)(5)-\frac{1}{2}(3)(3)$

$$
\begin{aligned}
& =\frac{1}{2}(25-9) \\
& =8
\end{aligned}
$$

Thus the required area is $8 \mathrm{~cm}^{2}$.

ANSWER: (B)