Pre-Algebra Student Edition
Pre-Algebra Student Edition
1st Edition
ISBN: 9780078957734
Author: Glencoe/McGraw-Hill
Publisher: MCG
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Chapter 11.9, Problem 20PPS
To determine

To calculate the area of the shaded region.

Expert Solution & Answer
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Answer to Problem 20PPS

  135 square feet.

Explanation of Solution

Given information:

The figure consists of a trapezoid along with a non-shaded triangle.

Trapezoid has sides a=18 feet, b=8 and the height would be calculated using Pythagoras theorem.

Triangle of b=8 feet and height would be calculated using Pythagoras theorem.

Formula used: Area of trapezoid t=a+b2×p , where ‘a’ and ‘b’ are parallel sides while ‘p’ is the perpendicular height.

Area of triangle s=12×b×p . Where ‘b’ is the base and ‘p’is the perpendicular height.

Pythagoras theorem will be used for finding the perpendicular height using p2+b2=h2 .

Here ‘p’ is the perpendicular height, ‘b’ is the base and ‘h’ is the hypotenuse of the right-angled triangle.

Calculation:

Calculate the height of the given figure first. This will enable to determine the overall area as well as the area of the non-shaded right-angle triangle present within the figure.

  p2+b2=h2

Using Pythagoras theorem.

  p2=h2b2

Since the value of the perpendicular height is needed, arrange the equation with keeping ‘p’ in the left-hand side.

  p=h2b2

On further simplification

  =17282

Putting the values in the expression.

  =28964

After this,

  =225

Taking the square root.

  p=15 feet.

Calculation of area of the figure, that is a trapezoid.

  t=a+b2×p

Putting the values in the equation.

  =18+82×15

On further simplification.

  =262×15

Multiplying

  =13×15

Total area

  =195 square feet.

Area of the unshaded triangle.

  s=12×b×p

Formula of area of the triangle.

  =12×8×15

Putting values in the formula.

  =4×15

Multiply the same.

  =60 square feet.

Area of shaded region

  =ts

Subtract area of unshaded region from area of complete figure.

  =19560

Subtracting the same.

  =135 square feet.

Chapter 11 Solutions

Pre-Algebra Student Edition

Ch. 11.1 - Prob. 7CYUCh. 11.1 - Prob. 8CYUCh. 11.1 - Prob. 9CYUCh. 11.1 - Prob. 10PPSCh. 11.1 - Prob. 11PPSCh. 11.1 - Prob. 12PPSCh. 11.1 - Prob. 13PPSCh. 11.1 - Prob. 14PPSCh. 11.1 - Prob. 15PPSCh. 11.1 - Prob. 16PPSCh. 11.1 - Prob. 17PPSCh. 11.1 - Prob. 18PPSCh. 11.1 - Prob. 19PPSCh. 11.1 - Prob. 20PPSCh. 11.1 - Prob. 21PPSCh. 11.1 - Prob. 22PPSCh. 11.1 - Prob. 23PPSCh. 11.1 - Prob. 24PPSCh. 11.1 - Prob. 25PPSCh. 11.1 - Prob. 26PPSCh. 11.1 - Prob. 27PPSCh. 11.1 - Prob. 28PPSCh. 11.1 - Prob. 29PPSCh. 11.1 - Prob. 30PPSCh. 11.1 - Prob. 31PPSCh. 11.1 - Prob. 32PPSCh. 11.1 - Prob. 33HPCh. 11.1 - Prob. 34HPCh. 11.1 - Prob. 35HPCh. 11.1 - Prob. 36HPCh. 11.1 - Prob. 37STPCh. 11.1 - Prob. 38STPCh. 11.1 - Prob. 39STPCh. 11.1 - Prob. 40STPCh. 11.1 - Prob. 41SRCh. 11.1 - Prob. 42SRCh. 11.1 - Prob. 43SRCh. 11.1 - Prob. 44SRCh. 11.1 - Prob. 45SRCh. 11.1 - Prob. 46SRCh. 11.1 - Prob. 47SCh. 11.1 - Prob. 48SCh. 11.1 - Prob. 49SCh. 11.1 - Prob. 50SCh. 11.1 - Prob. 51SCh. 11.2 - Prob. 1AGPCh. 11.2 - Prob. 1BGPCh. 11.2 - Prob. 2GPCh. 11.2 - Prob. 3GPCh. 11.2 - Prob. 1CYUCh. 11.2 - Prob. 2CYUCh. 11.2 - Prob. 3CYUCh. 11.2 - Prob. 4CYUCh. 11.2 - Prob. 5CYUCh. 11.2 - Prob. 6PPSCh. 11.2 - Prob. 7PPSCh. 11.2 - Prob. 8PPSCh. 11.2 - Prob. 9PPSCh. 11.2 - Prob. 10PPSCh. 11.2 - Prob. 11PPSCh. 11.2 - Prob. 12PPSCh. 11.2 - Prob. 13PPSCh. 11.2 - Prob. 14PPSCh. 11.2 - Prob. 15PPSCh. 11.2 - Prob. 16PPSCh. 11.2 - Prob. 17PPSCh. 11.2 - Prob. 18PPSCh. 11.2 - Prob. 19PPSCh. 11.2 - Prob. 20PPSCh. 11.2 - Prob. 21PPSCh. 11.2 - Prob. 22PPSCh. 11.2 - Prob. 23PPSCh. 11.2 - Prob. 24HPCh. 11.2 - Prob. 25HPCh. 11.2 - Prob. 26HPCh. 11.2 - Prob. 27HPCh. 11.2 - Prob. 28HPCh. 11.2 - Prob. 29STPCh. 11.2 - Prob. 30STPCh. 11.2 - Prob. 31STPCh. 11.2 - Prob. 32STPCh. 11.2 - Prob. 33SRCh. 11.2 - Prob. 34SRCh. 11.2 - Prob. 35SRCh. 11.2 - Prob. 36SRCh. 11.2 - Prob. 37SCh. 11.2 - Prob. 38SCh. 11.2 - Prob. 39SCh. 11.2 - Prob. 40SCh. 11.3 - Prob. 1AGPCh. 11.3 - Prob. 1BGPCh. 11.3 - Prob. 2GPCh. 11.3 - Prob. 3GPCh. 11.3 - Prob. 4GPCh. 11.3 - Prob. 1CYUCh. 11.3 - Prob. 2CYUCh. 11.3 - Prob. 3CYUCh. 11.3 - Prob. 4CYUCh. 11.3 - Prob. 5PPSCh. 11.3 - Prob. 6PPSCh. 11.3 - Prob. 7PPSCh. 11.3 - Prob. 8PPSCh. 11.3 - Prob. 9PPSCh. 11.3 - Prob. 10PPSCh. 11.3 - Prob. 11PPSCh. 11.3 - Prob. 12PPSCh. 11.3 - Prob. 13PPSCh. 11.3 - Prob. 14PPSCh. 11.3 - Prob. 15PPSCh. 11.3 - Prob. 16PPSCh. 11.3 - Prob. 17HPCh. 11.3 - Prob. 18HPCh. 11.3 - Prob. 19HPCh. 11.3 - Prob. 20HPCh. 11.3 - Prob. 21HPCh. 11.3 - Prob. 22STPCh. 11.3 - Prob. 23STPCh. 11.3 - Prob. 24STPCh. 11.3 - Prob. 25STPCh. 11.3 - Prob. 26SRCh. 11.3 - Prob. 27SRCh. 11.3 - Prob. 28SRCh. 11.3 - Prob. 29SCh. 11.3 - Prob. 30SCh. 11.3 - Prob. 31SCh. 11.4 - Prob. 1GPCh. 11.4 - Prob. 2GPCh. 11.4 - Prob. 1CYUCh. 11.4 - Prob. 2CYUCh. 11.4 - Prob. 3CYUCh. 11.4 - Prob. 4CYUCh. 11.4 - Prob. 5CYUCh. 11.4 - Prob. 6PPSCh. 11.4 - Prob. 7PPSCh. 11.4 - Prob. 8PPSCh. 11.4 - Prob. 9PPSCh. 11.4 - Prob. 10PPSCh. 11.4 - Prob. 11PPSCh. 11.4 - Prob. 12PPSCh. 11.4 - Prob. 13PPSCh. 11.4 - Prob. 14PPSCh. 11.4 - Prob. 15PPSCh. 11.4 - Prob. 16PPSCh. 11.4 - Prob. 17PPSCh. 11.4 - Prob. 18PPSCh. 11.4 - Prob. 19PPSCh. 11.4 - Prob. 20PPSCh. 11.4 - Prob. 21PPSCh. 11.4 - Prob. 22PPSCh. 11.4 - Prob. 23PPSCh. 11.4 - Prob. 24PPSCh. 11.4 - Prob. 25PPSCh. 11.4 - Prob. 26HPCh. 11.4 - Prob. 27HPCh. 11.4 - Prob. 28HPCh. 11.4 - Prob. 29HPCh. 11.4 - Prob. 30STPCh. 11.4 - Prob. 31STPCh. 11.4 - Prob. 32STPCh. 11.4 - Prob. 33STPCh. 11.4 - Prob. 34SRCh. 11.4 - Prob. 35SRCh. 11.4 - Prob. 36SRCh. 11.4 - Prob. 37SRCh. 11.4 - Prob. 38SRCh. 11.4 - Prob. 39SRCh. 11.4 - Prob. 40SRCh. 11.4 - Prob. 41SRCh. 11.4 - Prob. 42SCh. 11.4 - Prob. 43SCh. 11.4 - Prob. 44SCh. 11.4 - Prob. 45SCh. 11.5 - Prob. 1AGPCh. 11.5 - Prob. 1BGPCh. 11.5 - Prob. 2GPCh. 11.5 - Prob. 3GPCh. 11.5 - Prob. 4AGPCh. 11.5 - Prob. 4BGPCh. 11.5 - Prob. 1CYUCh. 11.5 - Prob. 2CYUCh. 11.5 - Prob. 3CYUCh. 11.5 - Prob. 4CYUCh. 11.5 - Prob. 5CYUCh. 11.5 - Prob. 6CYUCh. 11.5 - Prob. 7PPSCh. 11.5 - Prob. 8PPSCh. 11.5 - Prob. 9PPSCh. 11.5 - Prob. 10PPSCh. 11.5 - Prob. 11PPSCh. 11.5 - Prob. 12PPSCh. 11.5 - Prob. 13PPSCh. 11.5 - Prob. 14PPSCh. 11.5 - Prob. 15PPSCh. 11.5 - Prob. 16PPSCh. 11.5 - Prob. 17PPSCh. 11.5 - Prob. 18PPSCh. 11.5 - Prob. 19PPSCh. 11.5 - Prob. 20PPSCh. 11.5 - Prob. 21PPSCh. 11.5 - Prob. 22PPSCh. 11.5 - Prob. 23PPSCh. 11.5 - Prob. 24PPSCh. 11.5 - Prob. 25PPSCh. 11.5 - Prob. 26PPSCh. 11.5 - Prob. 27PPSCh. 11.5 - Prob. 28PPSCh. 11.5 - Prob. 29PPSCh. 11.5 - Prob. 30PPSCh. 11.5 - Prob. 31PPSCh. 11.5 - Prob. 32PPSCh. 11.5 - Prob. 33PPSCh. 11.5 - Prob. 34PPSCh. 11.5 - Prob. 35HPCh. 11.5 - Prob. 36HPCh. 11.5 - Prob. 37HPCh. 11.5 - Prob. 38HPCh. 11.5 - Prob. 39HPCh. 11.5 - Prob. 40STPCh. 11.5 - Prob. 41STPCh. 11.5 - Prob. 42STPCh. 11.5 - Prob. 43STPCh. 11.5 - Prob. 44SRCh. 11.5 - Prob. 45SRCh. 11.5 - Prob. 46SRCh. 11.5 - Prob. 47SRCh. 11.5 - Prob. 48SRCh. 11.5 - Prob. 49SRCh. 11.5 - Prob. 50SRCh. 11.5 - Prob. 51SRCh. 11.5 - Prob. 52SRCh. 11.5 - Prob. 53SRCh. 11.5 - Prob. 54SRCh. 11.5 - Prob. 55SRCh. 11.5 - Prob. 56SCh. 11.5 - Prob. 57SCh. 11.5 - Prob. 58SCh. 11.5 - Prob. 59SCh. 11.6 - Prob. 1AGPCh. 11.6 - Prob. 1BGPCh. 11.6 - Prob. 2AGPCh. 11.6 - Prob. 2BGPCh. 11.6 - Prob. 3GPCh. 11.6 - Prob. 1CYUCh. 11.6 - Prob. 2CYUCh. 11.6 - Prob. 3CYUCh. 11.6 - Prob. 4CYUCh. 11.6 - Prob. 5CYUCh. 11.6 - Prob. 6CYUCh. 11.6 - Prob. 7PPSCh. 11.6 - Prob. 8PPSCh. 11.6 - Prob. 9PPSCh. 11.6 - Prob. 10PPSCh. 11.6 - Prob. 11PPSCh. 11.6 - Prob. 12PPSCh. 11.6 - Prob. 13PPSCh. 11.6 - Prob. 14PPSCh. 11.6 - Prob. 15PPSCh. 11.6 - Prob. 16PPSCh. 11.6 - Prob. 17PPSCh. 11.6 - Prob. 18PPSCh. 11.6 - Prob. 19PPSCh. 11.6 - Prob. 20PPSCh. 11.6 - Prob. 21PPSCh. 11.6 - Prob. 22PPSCh. 11.6 - Prob. 23PPSCh. 11.6 - Prob. 24PPSCh. 11.6 - Prob. 25PPSCh. 11.6 - Prob. 26PPSCh. 11.6 - Prob. 27PPSCh. 11.6 - Prob. 28PPSCh. 11.6 - Prob. 29PPSCh. 11.6 - Prob. 30PPSCh. 11.6 - Prob. 31PPSCh. 11.6 - Prob. 32PPSCh. 11.6 - Prob. 33PPSCh. 11.6 - Prob. 34PPSCh. 11.6 - Prob. 35HPCh. 11.6 - Prob. 36HPCh. 11.6 - Prob. 37HPCh. 11.6 - Prob. 38HPCh. 11.6 - Prob. 39HPCh. 11.6 - Prob. 40STPCh. 11.6 - Prob. 41STPCh. 11.6 - Prob. 42STPCh. 11.6 - Prob. 43STPCh. 11.6 - Prob. 44SRCh. 11.6 - Prob. 45SRCh. 11.6 - Prob. 46SRCh. 11.6 - Prob. 47SRCh. 11.6 - Prob. 48SRCh. 11.6 - Prob. 49SRCh. 11.6 - Prob. 50SRCh. 11.6 - Prob. 51SRCh. 11.6 - Prob. 52SRCh. 11.6 - Prob. 53SRCh. 11.6 - Prob. 54SCh. 11.6 - Prob. 55SCh. 11.6 - Prob. 56SCh. 11.6 - Prob. 57SCh. 11.7 - Prob. 1AGPCh. 11.7 - Prob. 1BGPCh. 11.7 - Prob. 2GPCh. 11.7 - Prob. 3GPCh. 11.7 - Prob. 1CYUCh. 11.7 - Prob. 2CYUCh. 11.7 - Prob. 3CYUCh. 11.7 - Prob. 4CYUCh. 11.7 - Prob. 5CYUCh. 11.7 - Prob. 6CYUCh. 11.7 - Prob. 7PPSCh. 11.7 - Prob. 8PPSCh. 11.7 - Prob. 9PPSCh. 11.7 - Prob. 10PPSCh. 11.7 - Prob. 11PPSCh. 11.7 - Prob. 12PPSCh. 11.7 - Prob. 13PPSCh. 11.7 - Prob. 14PPSCh. 11.7 - Prob. 15PPSCh. 11.7 - Prob. 16PPSCh. 11.7 - Prob. 17PPSCh. 11.7 - Prob. 18PPSCh. 11.7 - Prob. 19PPSCh. 11.7 - Prob. 20PPSCh. 11.7 - Prob. 21PPSCh. 11.7 - Prob. 22PPSCh. 11.7 - Prob. 23PPSCh. 11.7 - Prob. 24PPSCh. 11.7 - Prob. 25HPCh. 11.7 - Prob. 26HPCh. 11.7 - Prob. 27HPCh. 11.7 - Prob. 28HPCh. 11.7 - Prob. 29HPCh. 11.7 - Prob. 30STPCh. 11.7 - Prob. 31STPCh. 11.7 - Prob. 32STPCh. 11.7 - Prob. 33STPCh. 11.7 - Prob. 34SRCh. 11.7 - Prob. 35SRCh. 11.7 - Prob. 36SRCh. 11.7 - Prob. 37SRCh. 11.7 - Prob. 38SRCh. 11.7 - Prob. 39SRCh. 11.7 - Prob. 40SRCh. 11.7 - Prob. 41SRCh. 11.7 - Prob. 42SCh. 11.7 - Prob. 43SCh. 11.7 - Prob. 44SCh. 11.8 - Prob. 1AGPCh. 11.8 - Prob. 1BGPCh. 11.8 - Prob. 2GPCh. 11.8 - Prob. 3GPCh. 11.8 - Prob. 1CYUCh. 11.8 - Prob. 2CYUCh. 11.8 - Prob. 3CYUCh. 11.8 - Prob. 4CYUCh. 11.8 - Prob. 5CYUCh. 11.8 - Prob. 6CYUCh. 11.8 - Prob. 7CYUCh. 11.8 - Prob. 8CYUCh. 11.8 - Prob. 9PPSCh. 11.8 - Prob. 10PPSCh. 11.8 - Prob. 11PPSCh. 11.8 - Prob. 12PPSCh. 11.8 - Prob. 13PPSCh. 11.8 - Prob. 14PPSCh. 11.8 - Prob. 15PPSCh. 11.8 - Prob. 16PPSCh. 11.8 - Prob. 17PPSCh. 11.8 - Prob. 18PPSCh. 11.8 - Prob. 19PPSCh. 11.8 - Prob. 20PPSCh. 11.8 - Prob. 21PPSCh. 11.8 - Prob. 22PPSCh. 11.8 - Prob. 23PPSCh. 11.8 - Prob. 24PPSCh. 11.8 - Prob. 25PPSCh. 11.8 - Prob. 26PPSCh. 11.8 - Prob. 27PPSCh. 11.8 - Prob. 28PPSCh. 11.8 - Prob. 29PPSCh. 11.8 - Prob. 30PPSCh. 11.8 - Prob. 31PPSCh. 11.8 - Prob. 32HPCh. 11.8 - Prob. 33HPCh. 11.8 - Prob. 34HPCh. 11.8 - Prob. 35HPCh. 11.8 - Prob. 36HPCh. 11.8 - Prob. 37STPCh. 11.8 - Prob. 38STPCh. 11.8 - Prob. 39STPCh. 11.8 - Prob. 40STPCh. 11.8 - Prob. 41SRCh. 11.8 - Prob. 42SRCh. 11.8 - Prob. 43SRCh. 11.8 - Prob. 44SRCh. 11.8 - Prob. 45SRCh. 11.8 - Prob. 46SRCh. 11.8 - Prob. 47SRCh. 11.8 - Prob. 48SCh. 11.8 - Prob. 49SCh. 11.8 - Prob. 50SCh. 11.8 - Prob. 51SCh. 11.9 - Prob. 1AGPCh. 11.9 - Prob. 1BGPCh. 11.9 - Prob. 2GPCh. 11.9 - Prob. 1CYUCh. 11.9 - Prob. 2CYUCh. 11.9 - Prob. 3CYUCh. 11.9 - Prob. 4CYUCh. 11.9 - Prob. 5CYUCh. 11.9 - Prob. 6PPSCh. 11.9 - Prob. 7PPSCh. 11.9 - Prob. 8PPSCh. 11.9 - Prob. 9PPSCh. 11.9 - Prob. 10PPSCh. 11.9 - Prob. 11PPSCh. 11.9 - Prob. 12PPSCh. 11.9 - Prob. 13PPSCh. 11.9 - Prob. 14PPSCh. 11.9 - Prob. 15PPSCh. 11.9 - Prob. 16PPSCh. 11.9 - Prob. 17PPSCh. 11.9 - Prob. 18PPSCh. 11.9 - Prob. 19PPSCh. 11.9 - Prob. 20PPSCh. 11.9 - Prob. 21PPSCh. 11.9 - Prob. 22PPSCh. 11.9 - Prob. 23HPCh. 11.9 - Prob. 24HPCh. 11.9 - Prob. 25HPCh. 11.9 - Prob. 26HPCh. 11.9 - Prob. 27STPCh. 11.9 - Prob. 28STPCh. 11.9 - Prob. 29STPCh. 11.9 - Prob. 30STPCh. 11.9 - Prob. 31SRCh. 11.9 - Prob. 32SRCh. 11.9 - Prob. 33SRCh. 11.9 - Prob. 34SRCh. 11.9 - Prob. 35SRCh. 11.9 - Prob. 36SRCh. 11.9 - Prob. 37SCh. 11.9 - Prob. 38SCh. 11.9 - Prob. 39SCh. 11.9 - Prob. 40SCh. 11 - Prob. 1QCCh. 11 - Prob. 2QCCh. 11 - Prob. 3QCCh. 11 - Prob. 4QCCh. 11 - Prob. 5QCCh. 11 - Prob. 6QCCh. 11 - Prob. 7QCCh. 11 - Prob. 8QCCh. 11 - Prob. 9QCCh. 11 - Prob. 10QCCh. 11 - Prob. 11QCCh. 11 - Prob. 12QCCh. 11 - Prob. 13QCCh. 11 - Prob. 14QCCh. 11 - Prob. 15QCCh. 11 - Prob. 16QCCh. 11 - Prob. 17QCCh. 11 - Prob. 18QCCh. 11 - Prob. 19QCCh. 11 - Prob. 20QCCh. 11 - Prob. 21QCCh. 11 - Prob. 1MCQCh. 11 - Prob. 2MCQCh. 11 - Prob. 3MCQCh. 11 - Prob. 4MCQCh. 11 - Prob. 5MCQCh. 11 - Prob. 6MCQCh. 11 - Prob. 7MCQCh. 11 - Prob. 8MCQCh. 11 - Prob. 9MCQCh. 11 - Prob. 10MCQCh. 11 - Prob. 11MCQCh. 11 - Prob. 12MCQCh. 11 - Prob. 13MCQCh. 11 - Prob. 14MCQCh. 11 - Prob. 15MCQCh. 11 - Prob. 16MCQCh. 11 - Prob. 1SGRCh. 11 - Prob. 2SGRCh. 11 - Prob. 3SGRCh. 11 - Prob. 4SGRCh. 11 - Prob. 5SGRCh. 11 - Prob. 6SGRCh. 11 - Prob. 7SGRCh. 11 - Prob. 8SGRCh. 11 - Prob. 9SGRCh. 11 - Prob. 10SGRCh. 11 - Prob. 11SGRCh. 11 - Prob. 12SGRCh. 11 - Prob. 13SGRCh. 11 - Prob. 14SGRCh. 11 - Prob. 15SGRCh. 11 - Prob. 16SGRCh. 11 - Prob. 17SGRCh. 11 - Prob. 18SGRCh. 11 - Prob. 19SGRCh. 11 - Prob. 20SGRCh. 11 - Prob. 21SGRCh. 11 - Prob. 22SGRCh. 11 - Prob. 23SGRCh. 11 - Prob. 24SGRCh. 11 - Prob. 25SGRCh. 11 - Prob. 26SGRCh. 11 - Prob. 27SGRCh. 11 - Prob. 28SGRCh. 11 - Prob. 29SGRCh. 11 - Prob. 30SGRCh. 11 - Prob. 31SGRCh. 11 - Prob. 32SGRCh. 11 - Prob. 33SGRCh. 11 - Prob. 34SGRCh. 11 - Prob. 35SGRCh. 11 - Prob. 36SGRCh. 11 - Prob. 37SGRCh. 11 - Prob. 38SGRCh. 11 - Prob. 39SGRCh. 11 - Prob. 40SGRCh. 11 - Prob. 41SGRCh. 11 - Prob. 1PTCh. 11 - Prob. 2PTCh. 11 - Prob. 3PTCh. 11 - Prob. 4PTCh. 11 - Prob. 5PTCh. 11 - Prob. 6PTCh. 11 - Prob. 7PTCh. 11 - Prob. 8PTCh. 11 - Prob. 9PTCh. 11 - Prob. 10PTCh. 11 - Prob. 11PTCh. 11 - Prob. 12PTCh. 11 - Prob. 13PTCh. 11 - Prob. 14PTCh. 11 - Prob. 15PTCh. 11 - Prob. 16PTCh. 11 - Prob. 1ECh. 11 - Prob. 2ECh. 11 - Prob. 3ECh. 11 - Prob. 4ECh. 11 - Prob. 1STPCh. 11 - Prob. 2STPCh. 11 - Prob. 3STPCh. 11 - Prob. 4STPCh. 11 - Prob. 5STPCh. 11 - Prob. 6STPCh. 11 - Prob. 7STPCh. 11 - Prob. 8STPCh. 11 - Prob. 9STPCh. 11 - Prob. 10STPCh. 11 - Prob. 11STPCh. 11 - Prob. 12STPCh. 11 - Prob. 13STPCh. 11 - Prob. 14STP
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