Trapezium

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# Trapezium

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In triangle ABC, two lines DE and FG are drawn parallel to BC such that they divide AC in the ratio 2:3:5. Find the ratio of area of triangle ABC to area of the trapezium DEGF.

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In a trapezium ABCD, AD||BC, ∠DAB and ∠ADC are acute angles. If AB and DC are extended to intersect at E and then perpendicular from E is drawn to AD. The perpendicular gets bisected by BC. If AB = 8 cm and AD = 10 cm, then what is the value of 2AC² + BD²?

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An equilateral triangle PQR of side 25 cm is divided into 2 parts such that one of them is an equilateral triangle containing one of the vertices of the original triangle and the other remaining part is a trapezium. What is the perimeter of the parallelogram formed when two such trapeziums are placed together?
A)Cannot be determined
B)100
C)200
D)150

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In a trapezium PQRS, PQ is parallel to RS, PQ = 20 cm, RS = 3 cm, PQR = 30° and QPS = 60°. What is the length of the line joining the midpoints of PQ and RS?

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The non-parallel sides of a trapezium of perimeter 34 cm are equal. The line segment joining the mid-points of the non-parallel sides is 12 cm. If the ratio of the area of the trapezium above this line to the area of the trapezium below this line is 7:9, what is the area of the trapezium?
A)24 cm²
B)128 cm²
C)48 cm²
D)96 cm²

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In a trapezium ABCD, AB||CD, AB = 2010 cm, CD = 1000 cm, ∠DAB = 40° and ∠ABC = 50°. What is the length of the line joining the midpoints of AB and CD?
1) 1000 cm
2) 1010 cm
3) 504 cm
4) 505 cm
5) None of these

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For a trapezium, S1 denotes the sum of the squares of the sides and S2 denotes the sum of the squares of the diagonals. S1 – S2 = 576. If the longer parallel side is 50 cm, the shorter parallel side is _______.

Options:

1.26 cm

2.22 cm

3.18 cm

4.30 cm

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The length of the line joining the midpoints of the non-parallel sides of an isosceles trapezium is 24. If the aforementioned line divides the trapezium in two parts with the areas in ratio 7 : 9, then what is the absolute difference (in cm) between the parallel sides of the trapezium?

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ABCD is a trapezium AB||CD . M is the mid point on AD and N on BC. O is the point on MN . Area of triangle BNO =4 cm² and DMO = 3cm² . What is the Area of ABCD ?

This post was modified 3 months ago by TG.Raman
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Given that AD // PQ // BC, and PQ divides Trapezium ABCD into two equal areas. Find the length of PQ.

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