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The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:
- a)74.98 cm2
- b)25.25 cm2
- c)75 cm2
- d)68.25 cm2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12...
s = a + b + c /2 = 12 + 9 + 15 /2 = 18cm
Area of PRS = √s(s - a)(s - b)(s - c) = 54 cm^2
s = a + b + c /2 = 7 + 6 + 9 /2 = 11 cm
Area of RPQ = √s(s - a)(s - b)(s - c) = 20.98 cm^2
Area of Quadrilateral = Area of RPQ + Area of PRS
= 54 + 20.98
= 74.98 cm^2
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The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12...
Given:
PQ = 7 cm
QR = 6 cm
RS = 12 cm
PS = 15 cm
PR = 9 cm
To find: Area of quadrilateral PQRS
Method:
We can divide the quadrilateral into two triangles, ∆PQR and ∆PSR.
Using Heron's formula, we can find the area of both triangles and then add them up to get the total area of the quadrilateral.
Heron's formula states that the area of a triangle whose sides are a, b, and c is given by:
area = √(s(s-a)(s-b)(s-c))
where s = (a+b+c)/2 is the semi-perimeter of the triangle.
Calculation:
For ∆PQR:
s = (PQ+QR+PR)/2 = (7+6+9)/2 = 11
area = √(11(11-7)(11-6)(11-9)) = √(11*4*5*2) = 22√10 cm²
For ∆PSR:
s = (PS+SR+PR)/2 = (15+12+9)/2 = 18
area = √(18(18-15)(18-12)(18-9)) = √(18*3*6*9) = 54 cm²
Total area of quadrilateral PQRS = area of ∆PQR + area of ∆PSR
= 22√10 + 54
= 74.98 cm² (approx)
Therefore, the correct option is (a) 74.98 cm².
PQ = 7 cm
QR = 6 cm
RS = 12 cm
PS = 15 cm
PR = 9 cm
To find: Area of quadrilateral PQRS
Method:
We can divide the quadrilateral into two triangles, ∆PQR and ∆PSR.
Using Heron's formula, we can find the area of both triangles and then add them up to get the total area of the quadrilateral.
Heron's formula states that the area of a triangle whose sides are a, b, and c is given by:
area = √(s(s-a)(s-b)(s-c))
where s = (a+b+c)/2 is the semi-perimeter of the triangle.
Calculation:
For ∆PQR:
s = (PQ+QR+PR)/2 = (7+6+9)/2 = 11
area = √(11(11-7)(11-6)(11-9)) = √(11*4*5*2) = 22√10 cm²
For ∆PSR:
s = (PS+SR+PR)/2 = (15+12+9)/2 = 18
area = √(18(18-15)(18-12)(18-9)) = √(18*3*6*9) = 54 cm²
Total area of quadrilateral PQRS = area of ∆PQR + area of ∆PSR
= 22√10 + 54
= 74.98 cm² (approx)
Therefore, the correct option is (a) 74.98 cm².
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The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:a)74.98 cm2b)25.25 cm2c)75 cm2d)68.25 cm2Correct answer is option 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:a)74.98 cm2b)25.25 cm2c)75 cm2d)68.25 cm2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:a)74.98 cm2b)25.25 cm2c)75 cm2d)68.25 cm2Correct answer is option 'A'. Can you explain this answer?.
The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:a)74.98 cm2b)25.25 cm2c)75 cm2d)68.25 cm2Correct answer is option 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:a)74.98 cm2b)25.25 cm2c)75 cm2d)68.25 cm2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:a)74.98 cm2b)25.25 cm2c)75 cm2d)68.25 cm2Correct answer is option 'A'. Can you explain this answer?.
Solutions for The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:a)74.98 cm2b)25.25 cm2c)75 cm2d)68.25 cm2Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:a)74.98 cm2b)25.25 cm2c)75 cm2d)68.25 cm2Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:a)74.98 cm2b)25.25 cm2c)75 cm2d)68.25 cm2Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:a)74.98 cm2b)25.25 cm2c)75 cm2d)68.25 cm2Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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