Constructing a Trapezium When Its Four Sides Are Given

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. 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. 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 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. 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. 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. Construct a trapezium ABCD in which $\overline{AB}$ is parallel to $\overline{DC}$ , AB = 10 cm, BC = 5 cm, AC = 8 cm and CD = 6 cm. Find 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 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