In trapezium ABCD,AB=14cm,AD=10cm,DC=xcm &distance between AB &DC is 8cm. find the value of x & area of the trapezium ABCD
Drop a perpendicular from D to AB, meeting it at P.
Then AP = 6 (Pythagorus)
Since we know nothing about BC, x can be anything from 0 to 8.
The area is (x+14)/2 * 8 = 4(x+14)
If the trapezium is isosceles, then x=2, but without some further knowledge, There's no way to pin down x.
To find the value of x and the area of trapezium ABCD, we can use the properties of a trapezium and the given information:
1. The length of AB is given as 14 cm.
2. The length of AD is given as 10 cm.
3. The distance between AB and DC is given as 8 cm.
Let's start by drawing the trapezium ABCD:
A----------------B
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D----------------C
Now, let's use the properties of a trapezium to find the value of x:
1. In a trapezium, the opposite sides are parallel. Therefore, AB || DC.
2. The distance between AB and DC is the perpendicular distance between the parallel sides.
3. The length of AD is a height drawn from point A perpendicular to DC.
Using these properties, we can create a right-angled triangle with sides AD, AB, and the distance between AB and DC:
A----------------B
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D----------------C
In this triangle, AB is the hypotenuse, AD is the perpendicular side, and the distance between AB and DC is the base.
We can use the Pythagorean theorem to find the length of DC:
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Applying this to our triangle, we have:
AB² = AD² + DC²
Plugging in the given values, we get:
14² = 10² + x²
196 = 100 + x²
x² = 196 - 100
x² = 96
x = √96
x ≈ 9.80 cm (rounded to two decimal places)
Therefore, the value of x is approximately 9.80 cm.
Next, let's find the area of trapezium ABCD using the formula:
Area = (sum of parallel sides) × (perpendicular distance between them) / 2
In this case, the parallel sides are AB and DC, and the perpendicular distance between them is 8 cm.
Area = (AB + DC) × distance / 2
Area = (14 + x) × 8 / 2
Area = (14 + 9.80) × 8 / 2
Area = 23.80 × 4
Area = 95.20 square cm
Therefore, the area of trapezium ABCD is 95.20 square cm.