Find the area and perimeter of each of the following: **Problem 15: Area Calculation of Compound Shapes**In this image, we have a compound shape that is essentially a rectangle with a smaller rectangular section removed from the top middle. The following dimensions are provided:- The width of the entire shape is 22 units.- The height of the entire shape is not directly given, but can be inferred from the provided measurements.- The removed rectangle on top has a width of 6 units and a height of 10 units.- The remaining widths at the top of the shape, on either side of the removed section, are both 8 units each.- The height of the main section (from the bottom to the top, excluding the removed section) is given as 10 units.**Steps to Calculate the Area:**1. **Calculate the area of the entire rectangle (including the removed section).** - Height of the entire rectangle is the height of the main section + height of the removed section which is 10 + 6 = 16 units. - Width of the entire rectangle is 22 units. - Therefore, area of the entire rectangle = 22 units * 16 units = 352 square units.2. **Calculate the area of the removed rectangle.** - The removed rectangle has a width of 6 units and a height of 10 units. - Therefore, the area of the removed rectangle = 6 units * 10 units = 60 square units.3. **Calculate the area of the compound shape.** - Area of compound shape = Area of the entire rectangle - Area of the removed rectangle. - Therefore, the area of the compound shape = 352 square units - 60 square units = 292 square units.**Graph Explanation:**- The graph is a basic line drawing representing the dimensions of a compound shape, composed of two rectangles.- The outer rectangle has dimensions of width 22 units and a combined height of 16 units (10 units for the main section and 6 units for the removed section).- A smaller rectangle (6 units by 10 units) is removed from the top part of the main rectangle.- The distances between various segments are labeled to aid in understanding the dimensions needed to calculate the area of the shape. This example is useful for understanding the concept of decomposing complex shapes into simpler ones to facilitate easier calculation of properties such as area.

Answered: Image /qna-images/answer/29250f61-50d7-48b9-a9dd-7ceb966fd28d.jpg

Answered: 8 8. 10 10 22 6.

Math

Geometry

8 8. 10 10 22 6.

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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