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Chapter 10: Q. 46 (page 824)

Use the results of Exercise 45 to find the areas of the quadrilaterals PQRSspecified in Exercises 46鈥�49.

role="math" localid="1649738595160" PQ=6,QR=7,RS=8,SP=9,PR=10

Short Answer

Expert verified

The areas of the quadrilaterals PQRSis localid="1649862103327" 54.85.

Step by step solution

01

Step 1. Given Information

Using the results of Exercise 45 we have to find the areas of the quadrilaterals PQRS:

PQ=6,QR=7,RS=8,SP=9,PR=10

02

Step 2. The Construction of quadrilateral by the given measurement is 

To find the area of quadrilateral we firstly finding the area of鈭�PQRand鈭�PSRthen add them.

03

Step 3. Now finding the area of ∆PQR.

The area of 鈭�PQR=s(s-a)(s-b)(s-c)

where s=a+b+c2

From the diagram a=6,b=7,c=10

Sos=6+7+102=232=11.5

04

Step 4. Putting the value of s in the formula of area.

Area鈭�PQR=s(s-a)(s-b)(s-c)Area鈭�PQR=11.5(11.5-6)(11.5-7)(11.5-10)Area鈭�PQR=11.5脳5.5脳4.5脳1.5Area鈭�PQR鈮�426.94Area鈭�PQR鈮�20.66

05

Step 5. Now finding the area of ∆PSR

From the diagrama=9,b=8,c=10

So

localid="1649861896902" s=9+8+102s=272s=13.5

06

Step 6. Putting the value of s in the formula of area.

Area鈭�PQR=s(s-a)(s-b)(s-c)Area鈭�PQR=13.5(13.5-9)(13.5-8)(13.5-10)Area鈭�PQR=13.5脳4.5脳5.5脳3.5Area鈭�PQR鈮�1169.44Area鈭�PQR鈮�34.19

07

Step 7. Now finding the area of quadrilateral PQRS

AreaofPQRS=Areaof鈭�PQR+Areaof鈭�PSRAreaofPQRS=20.66+34.19AreaofPQRS=54.85

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Most popular questions from this chapter

In Exercises 30鈥�35 compute the indicated quantities when u=(鈭�3,1,鈭�4),v=(2,0,5),andw=(1,3,13)

role="math" localid="1649434688557" v脳wandw脳v

Use calculator graphs to make approximations for each of the limits in Exercises 67鈥�74.

limx鈫�4(3-4x-5x2)

Find u+vandu-valso sketch u,v,u+v,u-v

role="math" localid="1649595165778" u=1,-2andv=-3,6

Write a delta鈥揺psilon proof that proves that fis continuous on its domain. In each case, you will need to assume that 未 is less than or equal to 1.

f(x)=x1/2

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(1,4,6),Q(鈭�3,5,0),R(3,2,鈭�1)
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