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In a quadrilateral, half of the product of the sum of the lengths of parallel sides and the parallel distance between them gives the area of
- a)rectangle
- b)parallelogram
- c)triangle
- d)trapezium
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In a quadrilateral, half of the product of the sum of the lengths of p...
Given that half of the product of the sum of the lengths of parallel sides and the parallel distance between them gives the area of a quadrilateral.
Let's consider the different types of quadrilaterals and see which one satisfies the given condition:
a) Rectangle:
A rectangle has two pairs of parallel sides, and the distance between them is the same for both pairs. Therefore, the sum of the lengths of parallel sides times the distance between them would be equal to the perimeter of the rectangle times its height, which is twice the area of the rectangle. Thus, the given condition is not satisfied for a rectangle.
b) Parallelogram:
A parallelogram also has two pairs of parallel sides, but the distance between them may not be the same for both pairs. However, we can draw a perpendicular from one side to the opposite side, which divides the parallelogram into two congruent triangles. The length of this perpendicular is the distance between the parallel sides. Thus, the sum of the lengths of parallel sides times the distance between them would be equal to the sum of the bases of the two triangles times their height, which is twice the area of the parallelogram. Therefore, the given condition is satisfied for a parallelogram.
c) Triangle:
A triangle has only one pair of parallel sides, and the distance between them is the height of the triangle. Therefore, the given condition is not satisfied for a triangle.
d) Trapezium:
A trapezium has two pairs of parallel sides, and the distance between them is different for both pairs. Therefore, the sum of the lengths of parallel sides times the distance between them would be equal to the sum of the areas of two triangles and a rectangle, which is twice the area of the trapezium. Thus, the given condition is satisfied for a trapezium.
Therefore, the correct answer is option 'D', which is trapezium.
Let's consider the different types of quadrilaterals and see which one satisfies the given condition:
a) Rectangle:
A rectangle has two pairs of parallel sides, and the distance between them is the same for both pairs. Therefore, the sum of the lengths of parallel sides times the distance between them would be equal to the perimeter of the rectangle times its height, which is twice the area of the rectangle. Thus, the given condition is not satisfied for a rectangle.
b) Parallelogram:
A parallelogram also has two pairs of parallel sides, but the distance between them may not be the same for both pairs. However, we can draw a perpendicular from one side to the opposite side, which divides the parallelogram into two congruent triangles. The length of this perpendicular is the distance between the parallel sides. Thus, the sum of the lengths of parallel sides times the distance between them would be equal to the sum of the bases of the two triangles times their height, which is twice the area of the parallelogram. Therefore, the given condition is satisfied for a parallelogram.
c) Triangle:
A triangle has only one pair of parallel sides, and the distance between them is the height of the triangle. Therefore, the given condition is not satisfied for a triangle.
d) Trapezium:
A trapezium has two pairs of parallel sides, and the distance between them is different for both pairs. Therefore, the sum of the lengths of parallel sides times the distance between them would be equal to the sum of the areas of two triangles and a rectangle, which is twice the area of the trapezium. Thus, the given condition is satisfied for a trapezium.
Therefore, the correct answer is option 'D', which is trapezium.
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In a quadrilateral, half of the product of the sum of the lengths of p...
Area of Rectangle = product of length and breadth (L * B)
Area of Parallelogram = A = ½ × d1 × d2 sin (y) where d1 & d2 are diagonal and y is the angle of intersection of diagonal.
Area of Trapezium = 1/2(sum of parallel sides)*height.
Area of Parallelogram = A = ½ × d1 × d2 sin (y) where d1 & d2 are diagonal and y is the angle of intersection of diagonal.
Area of Trapezium = 1/2(sum of parallel sides)*height.
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In a quadrilateral, half of the product of the sum of the lengths of parallel sides and the parallel distance between themgives the area ofa)rectangleb)parallelogramc)triangled)trapeziumCorrect answer is option 'D'. Can you explain this answer?
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