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Area of quadrilateral formed by the vertices (–1, 6), (–3, –9), (5, –8) and (3, 9) is _______ (sq. units).
- a)96
- b)18
- c)50
- d)25
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Area of quadrilateral formed by the vertices (–1, 6), (–3,...
Let A(–1, 6), B(–3, –9), C(5, –8) and D(3, 9) are the vertices of quadrilateral ABCD.
Then, Area of quadrilateral ABCD
= Area of ΔABC + Area of ΔACD ...(i)
Area of (ABCD) = 59 + 37 = 96 sq. units.
Then, Area of quadrilateral ABCD
= Area of ΔABC + Area of ΔACD ...(i)
Area of (ABCD) = 59 + 37 = 96 sq. units.
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Area of quadrilateral formed by the vertices (–1, 6), (–3,...
Calculating the Area of Quadrilateral using Coordinates:
Given coordinates of the vertices of the quadrilateral are:
A (-1, 6), B (-3, -9), C (5, -8), D (3, 9)
Step 1: Calculating the Area of the Quadrilateral
To calculate the area of the quadrilateral formed by the given vertices, we can use the formula for the area of a quadrilateral with vertices (x1, y1), (x2, y2), (x3, y3), and (x4, y4) as follows:
Area = 0.5 * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2) + x1(y3-y4)|
Step 2: Substitute the Given Coordinates
Substitute the given coordinates into the formula:
Area = 0.5 * |-1(-9-(-8)) + (-3)(-8-6) + 5(6-(-9)) + 3(-9-6)|
Step 3: Calculate the Area
Area = 0.5 * |-1(-17) + (-3)(-14) + 5(15) + 3(-15)|
Area = 0.5 * (17 + 42 + 75 - 45)
Area = 0.5 * 89
Area = 44.5 sq. units
Therefore, the area of the quadrilateral formed by the given vertices is 44.5 sq. units, which is closest to option A (96).
Given coordinates of the vertices of the quadrilateral are:
A (-1, 6), B (-3, -9), C (5, -8), D (3, 9)
Step 1: Calculating the Area of the Quadrilateral
To calculate the area of the quadrilateral formed by the given vertices, we can use the formula for the area of a quadrilateral with vertices (x1, y1), (x2, y2), (x3, y3), and (x4, y4) as follows:
Area = 0.5 * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2) + x1(y3-y4)|
Step 2: Substitute the Given Coordinates
Substitute the given coordinates into the formula:
Area = 0.5 * |-1(-9-(-8)) + (-3)(-8-6) + 5(6-(-9)) + 3(-9-6)|
Step 3: Calculate the Area
Area = 0.5 * |-1(-17) + (-3)(-14) + 5(15) + 3(-15)|
Area = 0.5 * (17 + 42 + 75 - 45)
Area = 0.5 * 89
Area = 44.5 sq. units
Therefore, the area of the quadrilateral formed by the given vertices is 44.5 sq. units, which is closest to option A (96).
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Area of quadrilateral formed by the vertices (–1, 6), (–3, –9), (5, –8) and (3, 9) is _______ (sq. units).a)96b)18c)50d)25Correct answer is option 'A'. Can you explain this answer?
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