### Problem 64:For the figure shown, (a) Use the Pythagorean theorem to find the length of the missing side, \( x \).(b) Compute the area of the triangular face.(c) Find the volume of the triangular prism.### Diagram Explanation:The diagram depicts a right triangular prism with one right-angled triangle face. The triangle face has the following dimensions:- One leg of the triangle is labeled as 8 cm.- The other leg of the triangle is unknown and is labeled as \( x \) cm.- The hypotenuse of the triangle is 12 cm.The length (depth) of the prism is given as 20 cm.

64. (R.4/1.1) For the figure shown, (a) use the Pythagorean theorem to find the length of the missing side, then compute (b) the area of the triangular face and (c) the volume of the triangular prism. 12 cm 8 cm 20 cm x cm

64. (R.4/1.1) For the figure shown, (a) use the Pythagorean theorem to find the length of the missing side, then compute (b) the area of the triangular face and (c) the volume of the triangular prism. 12 cm 8 cm 20 cm x cm

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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### Problem 64:

For the figure shown,

(a) Use the Pythagorean theorem to find the length of the missing side, \( x \).

(b) Compute the area of the triangular face.

(c) Find the volume of the triangular prism.

### Diagram Explanation:

The diagram depicts a right triangular prism with one right-angled triangle face. The triangle face has the following dimensions:

- One leg of the triangle is labeled as 8 cm.
- The other leg of the triangle is unknown and is labeled as \( x \) cm.
- The hypotenuse of the triangle is 12 cm.

The length (depth) of the prism is given as 20 cm.

Expert Solution

Step 1

We have to find

a) value of x which is stated in the figure with the help of Pythagorean theorem.

b) area of triangular region showed in the given fig.

c) volume of the triangular prism.

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