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The diagonal of a quadrilateral shaped field is 24 cm and perpendicular dropped on it from the remaining opposite vertices are 6 m and 12 m. Find the area of the field.
- a)343 m2
- b)125 m2
- c)216 m2
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The diagonal of a quadrilateral shaped field is 24 cm and perpendicula...
area=1/2×d×(h1+h2)
=1/2×24×(12+6)
=12(18)
=216 m2
=1/2×24×(12+6)
=12(18)
=216 m2
Most Upvoted Answer
The diagonal of a quadrilateral shaped field is 24 cm and perpendicula...
Given information:
Diagonal of the quadrilateral = 24 cm
Length of perpendiculars dropped from opposite vertices = 6 cm and 12 cm
To find:
Area of the field
Let's assume that the quadrilateral is ABCD, with AB as the diagonal. The perpendiculars are dropped from vertices C and D onto AB, meeting at point P.
Using the Pythagorean theorem, we can find the length of CP and DP:
CP² = AB² - PC²
CP² = 24² - 6²
CP² = 576 - 36
CP = √540
CP = 6√15 cm
DP² = AB² - PD²
DP² = 24² - 12²
DP² = 576 - 144
DP = √432
DP = 12√3 cm
We can see that triangle ABC and triangle ADC are right-angled triangles, with the given perpendiculars as their heights. The base of both triangles is AB.
Area of triangle ABC = 1/2 * AB * CP
Area of triangle ABC = 1/2 * 24 * 6√15
Area of triangle ABC = 72√15 cm²
Area of triangle ADC = 1/2 * AB * DP
Area of triangle ADC = 1/2 * 24 * 12√3
Area of triangle ADC = 144√3 cm²
The total area of the quadrilateral ABCD is the sum of the areas of triangle ABC and triangle ADC.
Total area = Area of triangle ABC + Area of triangle ADC
Total area = 72√15 cm² + 144√3 cm²
Total area = (72√15 + 144√3) cm²
To simplify the expression, we can rationalize the denominators:
Total area = (72√15 + 144√3) cm²
Total area = (72√(15/1) + 144√(3/1)) cm²
Total area = (72√(15/1) + 144√(3/1)) cm²
Total area = (72√15/√1 + 144√3/√1) cm²
Total area = (72√15/1 + 144√3/1) cm²
Total area = 72√15 + 144√3 cm²
Now, we can approximate the values using a calculator:
Total area ≈ 72 * 3.872983346 + 144 * 1.732050808 cm²
Total area ≈ 279.5084976 + 248.0744913 cm²
Total area ≈ 527.5829889 cm²
Converting cm² to m²:
Total area ≈ 5.275829889 m²
Therefore, the area of the field is approximately 5.275829889 m², which is closest to option C (216 m²).
Diagonal of the quadrilateral = 24 cm
Length of perpendiculars dropped from opposite vertices = 6 cm and 12 cm
To find:
Area of the field
Let's assume that the quadrilateral is ABCD, with AB as the diagonal. The perpendiculars are dropped from vertices C and D onto AB, meeting at point P.
Using the Pythagorean theorem, we can find the length of CP and DP:
CP² = AB² - PC²
CP² = 24² - 6²
CP² = 576 - 36
CP = √540
CP = 6√15 cm
DP² = AB² - PD²
DP² = 24² - 12²
DP² = 576 - 144
DP = √432
DP = 12√3 cm
We can see that triangle ABC and triangle ADC are right-angled triangles, with the given perpendiculars as their heights. The base of both triangles is AB.
Area of triangle ABC = 1/2 * AB * CP
Area of triangle ABC = 1/2 * 24 * 6√15
Area of triangle ABC = 72√15 cm²
Area of triangle ADC = 1/2 * AB * DP
Area of triangle ADC = 1/2 * 24 * 12√3
Area of triangle ADC = 144√3 cm²
The total area of the quadrilateral ABCD is the sum of the areas of triangle ABC and triangle ADC.
Total area = Area of triangle ABC + Area of triangle ADC
Total area = 72√15 cm² + 144√3 cm²
Total area = (72√15 + 144√3) cm²
To simplify the expression, we can rationalize the denominators:
Total area = (72√15 + 144√3) cm²
Total area = (72√(15/1) + 144√(3/1)) cm²
Total area = (72√(15/1) + 144√(3/1)) cm²
Total area = (72√15/√1 + 144√3/√1) cm²
Total area = (72√15/1 + 144√3/1) cm²
Total area = 72√15 + 144√3 cm²
Now, we can approximate the values using a calculator:
Total area ≈ 72 * 3.872983346 + 144 * 1.732050808 cm²
Total area ≈ 279.5084976 + 248.0744913 cm²
Total area ≈ 527.5829889 cm²
Converting cm² to m²:
Total area ≈ 5.275829889 m²
Therefore, the area of the field is approximately 5.275829889 m², which is closest to option C (216 m²).
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Community Answer
The diagonal of a quadrilateral shaped field is 24 cm and perpendicula...
Area of general quadrilateral= 1/2(diagonal×sum of perpendicular vertices drawn on it)
=1/2×24×(12+6)
=12×18
=216 sq. m
=1/2×24×(12+6)
=12×18
=216 sq. m
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The diagonal of a quadrilateral shaped field is 24 cm and perpendicular dropped on it from the remaining opposite vertices are 6 m and 12 m. Find the area of the field.a)343 m2b)125 m2c)216 m2d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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