Given:
The base of the prism is a right triangle with legs 1 m and 2 m.
The height of the prism is 17 m.
To find:
The volume of the given prism.
Solution:
The area of a triangle is:
![Area=(1)/(2)* base* height](https://img.qammunity.org/2022/formulas/mathematics/high-school/dg00k6k3o9wjc4fj90idlyq3kl3p8mv0jj.png)
So, the area of base of the prism is:
![Area=(1)/(2)* 1* 2](https://img.qammunity.org/2022/formulas/mathematics/high-school/yopx9lo856mlf4dia9ub0x06bxrukwwebn.png)
![Area=1](https://img.qammunity.org/2022/formulas/mathematics/high-school/6prvw9rwgis3heq438x4r95wu42ybc1prl.png)
Now, the volume of the prism is:
![V=Bh](https://img.qammunity.org/2022/formulas/mathematics/high-school/i0uoip5dxkt5l9ct07jmmbai46rixtevxu.png)
Where, B is the base area and h is the height of the prism.
Substituting
, we get
![V=(1)(17)](https://img.qammunity.org/2022/formulas/mathematics/high-school/bn2q0ee2b48nkwdcv5beu3dxp72r99nrc1.png)
![V=17](https://img.qammunity.org/2022/formulas/mathematics/high-school/cbbz8nepzk2687ryuwvrh91imhroxik37u.png)
The volume of the prism is 17 cubic m. Therefore, the correct option is (d).