Geometry For Enjoyment And Challenge
Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
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Chapter 11.8, Problem 1PSA

a.

To determine

To calculate:Thearea of triangle ABC .

a.

Expert Solution
Check Mark

Answer to Problem 1PSA

Thearea of triangle ABCis 6 .

Explanation of Solution

Given information:

In ΔABC

Side AB=3,

Side BC=4,

Side AC=5.

Formula used:

We can use Heron’s Formula to determine the area of a triangle when lengths of sides are given.

  s=a+b+c2

a , b and c are sides of triangle

Area of triangle:

  A=s(sa)(sb)(sc)

Calculation:

  Geometry For Enjoyment And Challenge, Chapter 11.8, Problem 1PSA , additional homework tip  1

AB , BC and CA are sides of triangle ABC .

  s=AB+BC+CA2=3+4+52=6

Area of triangle ABC :

  A=s(sa)(sb)(sc)A=6(63)(64)(65)A=6×3×2×1A=36A=6

b.

To determine

To find: The area of triangle DEF .

b.

Expert Solution
Check Mark

Answer to Problem 1PSA

The area of triangle DEF is 25 .

Explanation of Solution

Given information:

In ΔDEF

Side DE=3,

Side EF=3,

Side DF=4.

Formula used:

We can use Heron’s Formula to determine the area of a triangle when lengths of sides are given.

  s=a+b+c2

a , b and c are sides of triangle

Area of triangle:

  A=s(sa)(sb)(sc)

Calculation:

  Geometry For Enjoyment And Challenge, Chapter 11.8, Problem 1PSA , additional homework tip  2

DE , EF and DF are sides of triangle DEF .

  s=DE+EF+DF2=3+3+42=5

Area of triangle DEF :

  A=s(sa)(sb)(sc)A=5(53)(53)(54)A=5×2×2×1A=20A=25

c.

To determine

To find: The area of triangle LMN .

c.

Expert Solution
Check Mark

Answer to Problem 1PSA

The area of triangle LMN is 102 .

Explanation of Solution

Given information:

In ΔLMN

Side LM=5,

Side MN=6,

Side LN=9.

Formula used:

We can use Heron’s Formula to determine the area of a triangle when lengths of sides are given.

  s=a+b+c2

a , b and c are sides of triangle

Area of triangle:

  A=s(sa)(sb)(sc)

Calculation:

  Geometry For Enjoyment And Challenge, Chapter 11.8, Problem 1PSA , additional homework tip  3

LM , MN and LN are sides of triangle LMN .

  s=LM+MN+LN2=5+6+92=10

Area of triangle LMN :

  A=s(sa)(sb)(sc)A=10(105)(106)(109)A=10×5×4×1A=200A=102

d.

To determine

To find: The area of triangle OPQ .

d.

Expert Solution
Check Mark

Answer to Problem 1PSA

The area of triangle OPQ is 63 .

Explanation of Solution

Given information:

In ΔOPQ

Side OP=3,

Side PQ=7,

Side OQ=8.

Formula used:

We can use Heron’s Formula to determine the area of a triangle when lengths of sides are given.

  s=a+b+c2

a , b and c are sides of triangle

Area of triangle:

  A=s(sa)(sb)(sc)

Calculation:

  Geometry For Enjoyment And Challenge, Chapter 11.8, Problem 1PSA , additional homework tip  4

LM , MN and LN are sides of triangle LMN .

  s=OP+PQ+OQ2=3+7+82=9

Area of triangle LMN :

  A=s(sa)(sb)(sc)A=9(93)(97)(98)A=9×6×2×1A=108A=63

e.

To determine

To find: The area of triangle XYZ .

e.

Expert Solution
Check Mark

Answer to Problem 1PSA

The area of triangle XYZ is 60 .

Explanation of Solution

Given information:

In ΔXYZ

Side XY=8,

Side YZ=15,

Side XZ=17.

Formula used:

We can use Heron’s Formula to determine the area of a triangle when lengths of sides are given.

  s=a+b+c2

a , b and c are sides of triangle

Area of triangle:

  A=s(sa)(sb)(sc)

Calculation:

  Geometry For Enjoyment And Challenge, Chapter 11.8, Problem 1PSA , additional homework tip  5

XY , YZ and XZ are sides of triangle XYZ .

  s=XY+YZ+XZ2=8+15+172=20

Area of triangle XYZ :

  A=s(sa)(sb)(sc)A=20(208)(2015)(2017)A=20×12×5×3A=3600A=60

f.

To determine

To find: The area of triangle UVW .

f.

Expert Solution
Check Mark

Answer to Problem 1PSA

The area of triangle UVW is 84 .

Explanation of Solution

Given information:

In ΔUVW

Side UV=13,

Side VW=14,

Side UW=15.

Formula used:

We can use Heron’s Formula to determine the area of a triangle when lengths of sides are given.

  s=a+b+c2

a , b and c are sides of triangle

Area of triangle:

  A=s(sa)(sb)(sc)

Calculation:

  Geometry For Enjoyment And Challenge, Chapter 11.8, Problem 1PSA , additional homework tip  6

UV , VW and UW are sides of triangle UVW .

  s=UV+VW+UW2=13+14+152=21

Area of triangle UVW :

  A=s(sa)(sb)(sc)A=21(2113)(2114)(2115)A=21×8×7×6A=7056A=84

Chapter 11 Solutions

Geometry For Enjoyment And Challenge

Ch. 11.1 - Prob. 11PSBCh. 11.1 - Prob. 12PSBCh. 11.1 - Prob. 13PSBCh. 11.1 - Prob. 14PSBCh. 11.1 - Prob. 15PSBCh. 11.1 - Prob. 16PSCCh. 11.1 - Prob. 17PSCCh. 11.2 - Prob. 1PSACh. 11.2 - Prob. 2PSACh. 11.2 - Prob. 3PSACh. 11.2 - Prob. 4PSACh. 11.2 - Prob. 5PSACh. 11.2 - Prob. 6PSACh. 11.2 - Prob. 7PSACh. 11.2 - Prob. 8PSACh. 11.2 - Prob. 9PSACh. 11.2 - Prob. 10PSACh. 11.2 - Prob. 11PSACh. 11.2 - Prob. 12PSACh. 11.2 - Prob. 13PSBCh. 11.2 - Prob. 14PSBCh. 11.2 - Prob. 15PSBCh. 11.2 - Prob. 16PSBCh. 11.2 - Prob. 17PSBCh. 11.2 - Prob. 18PSBCh. 11.2 - Prob. 19PSBCh. 11.2 - Prob. 20PSBCh. 11.2 - Prob. 21PSBCh. 11.2 - Prob. 22PSBCh. 11.2 - Prob. 23PSBCh. 11.2 - Prob. 24PSBCh. 11.2 - Prob. 25PSBCh. 11.2 - Prob. 26PSCCh. 11.2 - Prob. 27PSCCh. 11.2 - Prob. 28PSCCh. 11.2 - Prob. 29PSCCh. 11.2 - Prob. 30PSCCh. 11.2 - Prob. 31PSCCh. 11.2 - Prob. 32PSCCh. 11.2 - Prob. 33PSCCh. 11.3 - Prob. 1PSACh. 11.3 - Prob. 2PSACh. 11.3 - Prob. 3PSACh. 11.3 - Prob. 4PSACh. 11.3 - Prob. 5PSACh. 11.3 - Prob. 6PSACh. 11.3 - Prob. 7PSBCh. 11.3 - Prob. 8PSBCh. 11.3 - Prob. 9PSBCh. 11.3 - Prob. 10PSBCh. 11.3 - Prob. 11PSBCh. 11.3 - Prob. 12PSBCh. 11.3 - Prob. 13PSBCh. 11.3 - Prob. 14PSCCh. 11.3 - Prob. 15PSCCh. 11.3 - Prob. 16PSCCh. 11.3 - Prob. 17PSCCh. 11.3 - Prob. 18PSCCh. 11.3 - Prob. 19PSCCh. 11.3 - Prob. 20PSCCh. 11.4 - Prob. 1PSACh. 11.4 - Prob. 2PSACh. 11.4 - Prob. 3PSACh. 11.4 - Prob. 4PSBCh. 11.4 - Prob. 5PSBCh. 11.4 - Prob. 6PSBCh. 11.4 - Prob. 7PSBCh. 11.4 - Prob. 8PSBCh. 11.4 - Prob. 9PSBCh. 11.4 - Prob. 10PSCCh. 11.4 - Prob. 11PSCCh. 11.4 - Prob. 12PSCCh. 11.4 - Prob. 13PSCCh. 11.5 - Prob. 1PSACh. 11.5 - Prob. 2PSACh. 11.5 - Prob. 3PSACh. 11.5 - Prob. 4PSACh. 11.5 - Prob. 5PSACh. 11.5 - Prob. 6PSACh. 11.5 - Prob. 7PSACh. 11.5 - Prob. 8PSACh. 11.5 - Prob. 9PSACh. 11.5 - Prob. 10PSACh. 11.5 - Prob. 11PSACh. 11.5 - Prob. 12PSBCh. 11.5 - Prob. 13PSBCh. 11.5 - Prob. 14PSBCh. 11.5 - Prob. 15PSBCh. 11.5 - Prob. 16PSBCh. 11.5 - Prob. 17PSBCh. 11.5 - Prob. 18PSBCh. 11.5 - Prob. 19PSCCh. 11.5 - Prob. 20PSCCh. 11.5 - Prob. 21PSCCh. 11.5 - Prob. 22PSCCh. 11.5 - Prob. 23PSCCh. 11.5 - Prob. 24PSCCh. 11.5 - Prob. 25PSCCh. 11.5 - Prob. 26PSCCh. 11.6 - Prob. 1PSACh. 11.6 - Prob. 2PSACh. 11.6 - Prob. 3PSACh. 11.6 - Prob. 4PSACh. 11.6 - Prob. 5PSACh. 11.6 - Prob. 6PSACh. 11.6 - Prob. 7PSACh. 11.6 - Prob. 8PSBCh. 11.6 - Prob. 9PSBCh. 11.6 - Prob. 10PSBCh. 11.6 - Prob. 11PSBCh. 11.6 - Prob. 12PSBCh. 11.6 - Prob. 13PSBCh. 11.6 - Prob. 14PSBCh. 11.6 - Prob. 15PSBCh. 11.6 - Prob. 16PSBCh. 11.6 - Prob. 17PSBCh. 11.6 - Prob. 18PSCCh. 11.6 - Prob. 19PSCCh. 11.6 - Prob. 20PSCCh. 11.6 - Prob. 21PSCCh. 11.6 - Prob. 22PSCCh. 11.6 - Prob. 23PSCCh. 11.7 - Prob. 1PSACh. 11.7 - Prob. 2PSACh. 11.7 - Prob. 3PSACh. 11.7 - Prob. 4PSACh. 11.7 - Prob. 5PSACh. 11.7 - Prob. 6PSACh. 11.7 - Prob. 7PSACh. 11.7 - Prob. 8PSACh. 11.7 - Prob. 9PSBCh. 11.7 - Prob. 10PSBCh. 11.7 - Prob. 11PSBCh. 11.7 - Prob. 12PSBCh. 11.7 - Prob. 13PSBCh. 11.7 - Prob. 14PSBCh. 11.7 - Prob. 15PSBCh. 11.7 - Prob. 16PSBCh. 11.7 - Prob. 17PSBCh. 11.7 - Prob. 18PSCCh. 11.7 - Prob. 19PSCCh. 11.7 - Prob. 20PSCCh. 11.7 - Prob. 21PSCCh. 11.7 - Prob. 22PSCCh. 11.8 - Prob. 1PSACh. 11.8 - Prob. 2PSACh. 11.8 - Prob. 3PSACh. 11.8 - Prob. 4PSBCh. 11.8 - Prob. 5PSBCh. 11.8 - Prob. 6PSBCh. 11.8 - Prob. 7PSBCh. 11.8 - Prob. 8PSBCh. 11.8 - Prob. 9PSBCh. 11.8 - Prob. 10PSBCh. 11.8 - Prob. 11PSCCh. 11.8 - Prob. 12PSCCh. 11.8 - Prob. 13PSCCh. 11 - Prob. 1RPCh. 11 - Prob. 2RPCh. 11 - Prob. 3RPCh. 11 - Prob. 4RPCh. 11 - Prob. 5RPCh. 11 - Prob. 6RPCh. 11 - Prob. 7RPCh. 11 - Prob. 8RPCh. 11 - Prob. 9RPCh. 11 - Prob. 10RPCh. 11 - Prob. 11RPCh. 11 - Prob. 12RPCh. 11 - Prob. 13RPCh. 11 - Prob. 14RPCh. 11 - Prob. 15RPCh. 11 - Prob. 16RPCh. 11 - Prob. 17RPCh. 11 - Prob. 18RPCh. 11 - Prob. 19RPCh. 11 - Prob. 20RPCh. 11 - Prob. 21RPCh. 11 - Prob. 22RPCh. 11 - Prob. 23RPCh. 11 - Prob. 24RPCh. 11 - Prob. 25RPCh. 11 - Prob. 26RPCh. 11 - Prob. 27RPCh. 11 - Prob. 28RPCh. 11 - Prob. 29RPCh. 11 - Prob. 30RPCh. 11 - Prob. 31RPCh. 11 - Prob. 32RPCh. 11 - Prob. 33RPCh. 11 - Prob. 34RPCh. 11 - Prob. 35RPCh. 11 - Prob. 36RPCh. 11 - Prob. 37RPCh. 11 - Prob. 38RPCh. 11 - Prob. 39RPCh. 11 - Prob. 40RPCh. 11 - Prob. 41RPCh. 11 - Prob. 42RPCh. 11 - Prob. 43RPCh. 11 - Prob. 44RPCh. 11 - Prob. 45RP
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