   Chapter 8.1, Problem 27E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# A beach tent is designed so that one side is open. Find the number of square feet of canvas needed to make the tent. To determine

To find:

The number of square feet of canvas needed to make the tent.

Explanation

1) Procedure:

Converting theoretical statement into mathematical statement, identifying the figure and the calculation is followed by suitable geometric formulae.

2) Calculation:

Given,

For the number of square feet of canvas we front side of the tent is open have to find the area of the tent

Back side of the tent is a rectangular shape and the top side of the tent is a parallelogram.

Find the area of the tent:

Left and right side of the tent is equal which is shown below.

Point B and D split the figure into two triangle with line BD¯

For the right ABD

Here, a=6ft and b=6ft

Area of the right triangle

ABD=12ab unit2

=12(6)(6)

=12(36)

=18 unit2.

For BCD

Base of BCD(b)=8ft

Height of BCD(h)=6ft

Area of the BCD

BCD=12bh unit2

BCD=12(8)(6)

=12(48)

=24ft

Area of the left side of tent (A1)=ABD+BCD

=18+24

A1=42ft2.

Thus, area of the right side A2=42ft2

Back side of the tent is triangular shape with equal dimensions of 12ft by 6ft

Area of the back side of tent (A3)=lw unit2

Where, length l=12ft and width w=6ft

A3=(12)(6)

A3=72ft2

Top side of the tent is an parallelogram with base 12 ft

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