Chapter 10: Q. 46 (page 824)

Use the results of Exercise 45 to find the areas of the quadrilaterals $P Q R S$ specified in Exercises 46–49.
role="math" localid="1649738595160" $P Q = 6, Q R = 7, R S = 8, S P = 9, P R = 10$

Short Answer

Expert verified

The areas of the quadrilaterals $P Q R S$ is localid="1649862103327" $54.85$ .

Step by step solution

Step 1. Given Information

Using the results of Exercise 45 we have to find the areas of the quadrilaterals $P Q R S$ :

$P Q = 6, Q R = 7, R S = 8, S P = 9, P R = 10$

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

To find the area of quadrilateral we firstly finding the area of $∆ P Q R and ∆ P S R$ then add them.

Step 3. Now finding the area of ∆PQR.

The area of $∆ P Q R = \sqrt{s (s - a) (s - b) (s - c)}$

where $s = \frac{a + b + c}{2}$

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

So $s = \frac{6 + 7 + 10}{2} = \frac{23}{2} = 11.5$

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

$Area ∆ P Q R = \sqrt{s (s - a) (s - b) (s - c)} Area ∆ P Q R = \sqrt{11.5 (11.5 - 6) (11.5 - 7) (11.5 - 10)} Area ∆ P Q R = \sqrt{11.5 \times 5.5 \times 4.5 \times 1.5} Area ∆ P Q R \approx \sqrt{426.94} Area ∆ P Q R \approx 20.66$

Step 5. Now finding the area of ∆PSR

From the diagram $a = 9, b = 8, c = 10$

localid="1649861896902" $s = \frac{9 + 8 + 10}{2} s = \frac{27}{2} s = 13.5$

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

$Area ∆ P Q R = \sqrt{s (s - a) (s - b) (s - c)} Area ∆ P Q R = \sqrt{13.5 (13.5 - 9) (13.5 - 8) (13.5 - 10)} Area ∆ P Q R = \sqrt{13.5 \times 4.5 \times 5.5 \times 3.5} Area ∆ P Q R \approx \sqrt{1169.44} Area ∆ P Q R \approx 34.19$

Step 7. Now finding the area of quadrilateral PQRS

$Area of P Q R S = Area of ∆ P Q R + Area of ∆ P S R Area of P Q R S = 20.66 + 34.19 Area of P Q R S = 54.85$

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Use the results of Exercise 45 to find the areas of the quadrilaterals $P Q R S$ specified in Exercises 46–49.
role="math" localid="1649738595160" $P Q = 6, Q R = 7, R S = 8, S P = 9, P R = 10$

Short Answer

Step by step solution

Step 1. Given Information

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

Step 3. Now finding the area of ∆PQR.

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

Step 5. Now finding the area of ∆PSR

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

Step 7. Now finding the area of quadrilateral PQRS

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Use the results of Exercise 45 to find the areas of the quadrilaterals PQRSspecified in Exercises 46–49.role="math" localid="1649738595160" PQ=6,QR=7,RS=8,SP=9,PR=10

Short Answer

Step by step solution

Step 1. Given Information

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

Step 3. Now finding the area of ∆PQR.

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

Step 5. Now finding the area of ∆PSR

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

Step 7. Now finding the area of quadrilateral PQRS

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

Use the results of Exercise 45 to find the areas of the quadrilaterals $P Q R S$ specified in Exercises 46–49.
role="math" localid="1649738595160" $P Q = 6, Q R = 7, R S = 8, S P = 9, P R = 10$