What is the area of this Triangle **Educational Content on Triangle Areas**Understanding the area of a triangle is a fundamental aspect of geometry. Below is an example problem for practice:---**Problem: Calculating the Area of a Triangle***Question:*What is the area of this triangle?*Diagram Description:*The diagram includes a right triangle divided into two smaller right triangles. It is composed of the following measurements:- Left vertical side: 9 inches (in)- Right vertical side: 13 inches (in)- Middle horizontal segment (altitude from the vertical division of the base): 7 inches (in)- Entire base of the triangle: 18 inches (in)*Multiple Choice Options:*- 47 in²- 63 in²- 162 in²- 14,742 in²To calculate the area of a triangle, the formula used is:\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]In this problem, the base of the triangle is 18 inches, and the height (the perpendicular segment) is 7 inches. Applying these values to the formula:\[ \text{Area} = \frac{1}{2} \times 18 \text{ in} \times 7 \text{ in} \]\[ \text{Area} = \frac{1}{2} \times 126 \text{ in}^2 \]\[ \text{Area} = 63 \text{ in}^2 \]Thus, the correct answer is:- 63 in²This practical example helps illustrate how to apply basic geometric principles to calculate the area of a triangle efficiently.

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Answered: What is the Area of this 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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What is the area of this Triangle

**Educational Content on Triangle Areas**

Understanding the area of a triangle is a fundamental aspect of geometry. Below is an example problem for practice:

---

**Problem: Calculating the Area of a Triangle**

*Question:*
What is the area of this triangle?

*Diagram Description:*
The diagram includes a right triangle divided into two smaller right triangles. It is composed of the following measurements:
- Left vertical side: 9 inches (in)
- Right vertical side: 13 inches (in)
- Middle horizontal segment (altitude from the vertical division of the base): 7 inches (in)
- Entire base of the triangle: 18 inches (in)

*Multiple Choice Options:*
- 47 in²
- 63 in²
- 162 in²
- 14,742 in²

To calculate the area of a triangle, the formula used is:

\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

In this problem, the base of the triangle is 18 inches, and the height (the perpendicular segment) is 7 inches. Applying these values to the formula:

\[ \text{Area} = \frac{1}{2} \times 18 \text{ in} \times 7 \text{ in} \]
\[ \text{Area} = \frac{1}{2} \times 126 \text{ in}^2 \]
\[ \text{Area} = 63 \text{ in}^2 \]

Thus, the correct answer is:
- 63 in²

This practical example helps illustrate how to apply basic geometric principles to calculate the area of a triangle efficiently.

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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