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.

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?

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

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?

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

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

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

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?

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 ?

Given that AD // PQ // BC, and PQ divides Trapezium ABCD into two equal areas. Find the length of PQ.