What is the area of the triangle? ### Right Triangle and its ComponentsThe diagram exemplifies a right triangle with specific measurements labeled for its sides. This explanatory text is aimed at guiding students through the essential components and dimensions of the triangle as illustrated.**Description of the Diagram:**- **Hypotenuse:** The longest side of the right triangle is labeled as "10 feet."- **Other Sides:** - One leg of the triangle is labeled as "7.8 feet." - The shorter leg adjacent to the right angle (forming one of the triangle's sides) is labeled as "8 feet." - Another segment perpendicular to the 8-feet side inside the triangle is labeled as "5 feet." - The height of the triangle from the base to the hypotenuse is labeled as "6 feet."**Explanation:**- The diagram contains two right triangles within the original right triangle separated by a dashed vertical line, which represents the height (6 feet) dropping perpendicular from the hypotenuse.- One smaller triangle formed has sides 7.8 feet and 5 feet.- The base of the original right triangle between the perpendicular height and the right angle is 8 feet.This construction illustrates how a larger right triangle can be divided into two smaller ones, maintaining the right angle in both parts. It aids in applying geometric principles such as the Pythagorean theorem, which relates the lengths of the sides in right triangles:\[ a^2 + b^2 = c^2 \]where $ a $ and $ b $ represent the lengths of the legs of the triangle, and $ c $ represents the length of the hypotenuse. This particular triangle's layout sets a perfect example to explore geometric proofs and calculations.

The given figure is, The height of the triangle is 6 ft. And, the base of the triangle is 13 ft.

Answered: What is the area of the triangle?

Math

Geometry

What is the area of the triangle?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

What is the area of the triangle?

### Right Triangle and its Components

The diagram exemplifies a right triangle with specific measurements labeled for its sides. This explanatory text is aimed at guiding students through the essential components and dimensions of the triangle as illustrated.

**Description of the Diagram:**
- **Hypotenuse:** The longest side of the right triangle is labeled as "10 feet."
- **Other Sides:**
- One leg of the triangle is labeled as "7.8 feet."
- The shorter leg adjacent to the right angle (forming one of the triangle's sides) is labeled as "8 feet."
- Another segment perpendicular to the 8-feet side inside the triangle is labeled as "5 feet."
- The height of the triangle from the base to the hypotenuse is labeled as "6 feet."

**Explanation:**
- The diagram contains two right triangles within the original right triangle separated by a dashed vertical line, which represents the height (6 feet) dropping perpendicular from the hypotenuse.
- One smaller triangle formed has sides 7.8 feet and 5 feet.
- The base of the original right triangle between the perpendicular height and the right angle is 8 feet.

This construction illustrates how a larger right triangle can be divided into two smaller ones, maintaining the right angle in both parts. It aids in applying geometric principles such as the Pythagorean theorem, which relates the lengths of the sides in right triangles:

\[ a^2 + b^2 = c^2 \]

where $ a $ and $ b $ represent the lengths of the legs of the triangle, and $ c $ represents the length of the hypotenuse. This particular triangle's layout sets a perfect example to explore geometric proofs and calculations.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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