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A park, in the shape of quadrilateral ABCD, has angleB=90 degree, AB=9cm BC=12cm CD=5cm and AD=8cm.How many area will it occupy ?
Most Upvoted Answer
A park, in the shape of quadrilateral ABCD, has angleB=90 degree, AB=9...
∠C = 90º, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m
Joim BD
In ΔBCD,
By applying Pythagoras theorem,
BD2 = BC2 + CD2
⇒ BD2 = 122 + 52
⇒ BD2 = 169
⇒ BD = 13 m
Area of ΔBCD = 1/2 × 12 × 5 = 30 m2
Now,
Semi perimeter of ΔABD(s) = (8 + 9 + 13)/2 m = 30/2 m = 15 m
Using heron's formula,
Area of ΔABD = √s (s-a) (s-b) (s-c)
= √15(15 - 13) (15 - 9) (15 - 8) m2
= √15 × 2 × 6 × 7 m2
= 6√35 m2 = 35.5 m2 (approx)
Area of quadrilateral ABCD = Area of ΔBCD + Area of ΔABD = 30 m2 + 35.5m2 = 65.5m2
Joim BD
In ΔBCD,
By applying Pythagoras theorem,
BD2 = BC2 + CD2
⇒ BD2 = 122 + 52
⇒ BD2 = 169
⇒ BD = 13 m
Area of ΔBCD = 1/2 × 12 × 5 = 30 m2
Now,
Semi perimeter of ΔABD(s) = (8 + 9 + 13)/2 m = 30/2 m = 15 m
Using heron's formula,
Area of ΔABD = √s (s-a) (s-b) (s-c)
= √15(15 - 13) (15 - 9) (15 - 8) m2
= √15 × 2 × 6 × 7 m2
= 6√35 m2 = 35.5 m2 (approx)
Area of quadrilateral ABCD = Area of ΔBCD + Area of ΔABD = 30 m2 + 35.5m2 = 65.5m2
Community Answer
A park, in the shape of quadrilateral ABCD, has angleB=90 degree, AB=9...
Calculating the Area of the Park:
- Step 1: Find the Area of Triangle ABC
- Calculate the semi-perimeter of triangle ABC: s = (AB + BC + AC) / 2
- s = (9 + 12 + √(9^2 + 12^2)) / 2
- s = 15.5 cm
- Use Heron's formula to find the area of triangle ABC:
- Area(ABC) = √(s(s-AB)(s-BC)(s-AC))
- Area(ABC) = √(15.5(15.5-9)(15.5-12)(15.5-√(9^2 + 12^2)))
- Area(ABC) ≈ 41.44 cm²
- Step 2: Find the Area of Triangle ACD
- Calculate the semi-perimeter of triangle ACD: s = (AD + CD + AC) / 2
- s = (8 + 5 + √(8^2 + 5^2)) / 2
- s = 10.5 cm
- Use Heron's formula to find the area of triangle ACD:
- Area(ACD) = √(s(s-AD)(s-CD)(s-AC))
- Area(ACD) = √(10.5(10.5-8)(10.5-5)(10.5-√(8^2 + 5^2)))
- Area(ACD) ≈ 17.5 cm²
- Step 3: Find the Area of Quadrilateral ABCD
- Area(ABCD) = Area(ABC) + Area(ACD)
- Area(ABCD) ≈ 41.44 + 17.5
- Area(ABCD) ≈ 58.94 cm²
Therefore, the park will occupy an area of approximately 58.94 cm².
- Step 1: Find the Area of Triangle ABC
- Calculate the semi-perimeter of triangle ABC: s = (AB + BC + AC) / 2
- s = (9 + 12 + √(9^2 + 12^2)) / 2
- s = 15.5 cm
- Use Heron's formula to find the area of triangle ABC:
- Area(ABC) = √(s(s-AB)(s-BC)(s-AC))
- Area(ABC) = √(15.5(15.5-9)(15.5-12)(15.5-√(9^2 + 12^2)))
- Area(ABC) ≈ 41.44 cm²
- Step 2: Find the Area of Triangle ACD
- Calculate the semi-perimeter of triangle ACD: s = (AD + CD + AC) / 2
- s = (8 + 5 + √(8^2 + 5^2)) / 2
- s = 10.5 cm
- Use Heron's formula to find the area of triangle ACD:
- Area(ACD) = √(s(s-AD)(s-CD)(s-AC))
- Area(ACD) = √(10.5(10.5-8)(10.5-5)(10.5-√(8^2 + 5^2)))
- Area(ACD) ≈ 17.5 cm²
- Step 3: Find the Area of Quadrilateral ABCD
- Area(ABCD) = Area(ABC) + Area(ACD)
- Area(ABCD) ≈ 41.44 + 17.5
- Area(ABCD) ≈ 58.94 cm²
Therefore, the park will occupy an area of approximately 58.94 cm².
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A park, in the shape of quadrilateral ABCD, has angleB=90 degree, AB=9cm BC=12cm CD=5cm and AD=8cm.How many area will it occupy ?
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A park, in the shape of quadrilateral ABCD, has angleB=90 degree, AB=9cm BC=12cm CD=5cm and AD=8cm.How many area will it occupy ? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A park, in the shape of quadrilateral ABCD, has angleB=90 degree, AB=9cm BC=12cm CD=5cm and AD=8cm.How many area will it occupy ? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A park, in the shape of quadrilateral ABCD, has angleB=90 degree, AB=9cm BC=12cm CD=5cm and AD=8cm.How many area will it occupy ?.
A park, in the shape of quadrilateral ABCD, has angleB=90 degree, AB=9cm BC=12cm CD=5cm and AD=8cm.How many area will it occupy ? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A park, in the shape of quadrilateral ABCD, has angleB=90 degree, AB=9cm BC=12cm CD=5cm and AD=8cm.How many area will it occupy ? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A park, in the shape of quadrilateral ABCD, has angleB=90 degree, AB=9cm BC=12cm CD=5cm and AD=8cm.How many area will it occupy ?.
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