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What is the area of the figure? The figure is not drawn to scale. A. 144.5cm B. 127cm C. 172cm D. 50cm

What is the area of the figure? The figure is not drawn to scale. A. 144.5cm B. 127cm C. 172cm D. 50cm

Elementary Geometry For College Students, 7e
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 the figure? The figure is not drawn to scale.

A. 144.5cm

B. 127cm

C. 172cm

D. 50cm

**Understanding Geometric Shapes: Composite Figures** This diagram demonstrates a composite figure consisting of a rectangle attached to a right triangle. 1. **Rectangle:** - The rectangle has a height of **13 cm** and a width of **9 cm**. - All four internal angles of the rectangle are right angles (90 degrees). - The properties of the rectangle include parallel opposite sides and equal opposite sides. 2. **Right Triangle:** - The right triangle is positioned adjacent to one of the shorter sides of the rectangle. - The leg of the right triangle that is part of the rectangle's shorter side measures **8 cm**. - The base of the triangle, the side lying on the same plane as the rectangle's longer side, measures **11 cm**. - The right angle of the triangle is formed at the intersection where the 8 cm side meets the 11 cm side. **Detailed Explanation of Each Component:** - The **rectangle**: - Top side length: 9 cm - Bottom side length: 9 cm - Left side length: 13 cm - Right side length: 13 cm Each internal angle is denoted by a small square at the corners, indicating the 90-degree right angles. - The **right triangle**: - One leg aligns with the bottom of the rectangle (8 cm, representing the vertical height when joined at the base). - The other leg represents the base of the triangle, which is 11 cm long. - The hypotenuse is not labeled but extends from the top of the 8 cm leg to the outer end of the 11 cm base. By examining this diagram, one can explore various geometric concepts such as calculating the area and perimeter of composite figures, understanding right angles, and identifying properties of rectangles and right triangles.
Transcribed Image Text:**Understanding Geometric Shapes: Composite Figures** This diagram demonstrates a composite figure consisting of a rectangle attached to a right triangle. 1. **Rectangle:** - The rectangle has a height of **13 cm** and a width of **9 cm**. - All four internal angles of the rectangle are right angles (90 degrees). - The properties of the rectangle include parallel opposite sides and equal opposite sides. 2. **Right Triangle:** - The right triangle is positioned adjacent to one of the shorter sides of the rectangle. - The leg of the right triangle that is part of the rectangle's shorter side measures **8 cm**. - The base of the triangle, the side lying on the same plane as the rectangle's longer side, measures **11 cm**. - The right angle of the triangle is formed at the intersection where the 8 cm side meets the 11 cm side. **Detailed Explanation of Each Component:** - The **rectangle**: - Top side length: 9 cm - Bottom side length: 9 cm - Left side length: 13 cm - Right side length: 13 cm Each internal angle is denoted by a small square at the corners, indicating the 90-degree right angles. - The **right triangle**: - One leg aligns with the bottom of the rectangle (8 cm, representing the vertical height when joined at the base). - The other leg represents the base of the triangle, which is 11 cm long. - The hypotenuse is not labeled but extends from the top of the 8 cm leg to the outer end of the 11 cm base. By examining this diagram, one can explore various geometric concepts such as calculating the area and perimeter of composite figures, understanding right angles, and identifying properties of rectangles and right triangles.
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