Constructing a Trapezium When Its Four Sides Are Given

Q. Find the length of AB, if the length of BD is 6 cm and AO is one third of AC which 12 cm.

1. 3 cm
2. 4 cm
3. 5 cm
4. 6 cm

Q.

Two parallel sides of a trapezium are 58 cm and 42 cm. The other two sides are of equal length which is 17cm. Find the area of the trapezium.

1. $1500c{m}^2$

2. $750cm$

3. $325c{m}^2$

4. $750c{m}^2$

Q.

Construct a quadrilateral with three sides and two angles given.

Q.

A trapezium has an area of 570 cm², the height of the trapezium is 5 cm and the larger parallel side is twice in length as the smaller parallel side.Choose the correct option.

1. Length of the larger side is 152 cm

2. Length of the smaller side is 76cm

3. Difference in the length of parallel sides is 76 cm

4. All of these

Q.

An isosceles trapezium has an area of 36 cm², the parallel sides are 12 cm and 6 cm respectively. The perimeter of the trapezium should be ___cm.

Q. In an isosceles trapezium ABCD, AB||DC and AD=BC.If angle D=60^°, AB=18cm and AD=12 cm, find the length of DC.

Q. In trapezium ABCD, AB II CD. AB = 10cm, CD = 7cm, AD = 3cm and BC = 3cm. Find the approximate length of the perpendicular drawn from C to AB.

1. 3.5cm
2. 4cm
3. 1cm
4. 2.6cm

Q. Construct the trapeziums with the given measures and also find their area.
AIMS with AI || SM, AI = 6 cm, IM = 5 cm, AM = 9 cm and MS = 6.5 cm
$\left[5\right]$

Q.

When constructing a trapezium if 2 sides are given, a minimum of how many angles need to be provided?

__

Q. Construct a trapezium whose sides are given to be $10cm,4cm,6cm$ and $3cm$ such that the sides of length $10cm$ and $6cm$ are parallel. Then the measure of the base angles are:

1. ${38}^{\circ },{83}^{\circ }$
2. ${44}^{\circ },{83}^{\circ }$
3. ${44}^{\circ },{68}^{\circ }$
4. ${38}^{\circ },{68}^{\circ }$

Q. Suppose you are given the lengths of all 4 sides and the sides which are parallel are specified, how many trapeziums can you draw?

1. 1
2. 3
3. Data insufficient
4. 2

Q. A trapezium can be constructed by constructing a triangle and then a parallelogram. State True or False.

1. False
2. True

Q. If two diagonals of an isosceles trapezium are $3xcm$ and $(2x+2)cm$. Find the value of $x$.

1. 1
2. 2
3. 3
4. 4

Q.

A trapezium has an area of 570 cm². The height of the trapezium is 5 cm and the larger parallel side is twice in length as the smaller parallel side.Choose the correct option.

1. Length of the larger side is 152 cm

2. Length of the smaller side is 76cm

3. Length of the smaller side is 38 cm
4. Length of the larger side is 76 cm

Q. Construct a trapezium ABCD with dimensions $AB=8cm,BC=5cm,AC=6cm,CD=4.5cm$ and AB is parallel to CD. Find the area of the trapezium (in sq cm.).

1. $23.5$
2. $22.5$
3. $26.5$
4. None of these

Q. Which of the following properties are used in the construction of a trapezium when all four sides are given?

1. One pair of opposite sides are parallel
2. The two non-parallel sides are unequal.
3. Adjacent angles are supplementary.
4. The diagonals do not bisect each other.

Q. Construct an isosceles trapezium ABCD in which $\overline{AB}$ is parallel to $\overline{DC}$ , AB = 11 cm, DC = 7 cm, AD = BC = 6 cm and calculate its area.

Q.

The area of a trapezium is $91c{m}^2$ and its height is $7cm$. If one of the parallel sides is longer than the other by $8cm$, find the sum of the length of two parallel sides (in $cm$).

Q. Construct a trapezium having parallel sides $25$ cm and $13$ cm; its nonparallel sides are equal, each being $10$ cm. Find the area of the trapezium (in sq. cm).

1. $148$
2. $152$
3. $158$
4. None of these

Q. Construct a quadrilateral $PQRS$ where $PQ=4$cm, $QR=6$cm, $RS=5$cm, $PS=5.5$cm and $PR=7$cm

Q.

Construct a trapezium with the parallel sides in the ratio of $2:1$. If the distance between the parallel sides is $6$ cm and the area is $135$ sq cm, Find the length of parallel sides ( in cm ).

1. $15,30$
2. $16,28$
3. $18,26$
4. None of these

Q. In the figure, AB and DC are parallel sides of a trapezium $ABCD$ and $\angle ADC={90}^o$. Given $AB=15cm,CD=40cm$ and diagonal $AC=41cm$, calculate the area of trapezium ABCD

Q. Construct a trapezium ABCD with dimensions $AB=8cm,BC=5cm,AC=6cm,CD=4.5cm$ and $AB$ is parallel to $CD$. Find the height of the trapezium (in cm.).

1. $4.2$
2. $3.8$
3. $3.6$
4. None of these

Q. Consider a trapezium $ABCD$ with $AB=8cm,BC=AD=5cm,$ and $CD=2cm$. It has an altitude $CE=8cm$ on line $AB$. Find the area of the trapezium.

1. $25c{m}^2$
2. $50c{m}^2$
3. $40c{m}^2$
4. $10c{m}^2$

Q. On a flat road, a company needs to construct a flyover for smooth traffic. The flyover will be at an angle of ${37}^0$ to the flat road. The road leading up to the flyover and back down to the flat road are each of $50m$. The horizontal part of the flyover will be $100m$ in length. Find the length (in $m$) of the old road on which this flyover construction is scheduled.

Q. In trapezium ABCD, AB II CD. AB = 10 cm, CD = 7 cm, AD = 3 cm and BC = 3 cm. Find the approximate length of the perpendicular drawn from C to AB.

1. 1 cm
2. 4 cm
3. 2.6 cm
4. 3.5 cm

Q. Question 10
Which of the following properties describe a trapezium?
a) A pair of opposite sides is parallel
b) The diagonals bisect each other
c) The diagonals are perpendicular to each other
d) The diagonals are equal

Q. Construct a trapezium ABCD in which AB || DC , $\angle$ A $={105}^{\circ }$ , AD $=3cm$ , AB $=4cm$ and CD $=8cm$.

Q. Which property is used in the construction of a trapezium given the lengths of 3 sides and one of the angles?

Q.

A trapezium has an area of 570 cm². The height of the trapezium is 5 cm and the larger parallel side is twice in length as the smaller parallel side.Choose the correct option.

1. Length of the larger side is 152 cm

2. Length of the smaller side is 76cm

3. Length of the smaller side is 38 cm
4. Length of the larger side is 76 cm