Constructing a Trapezium When Its Two Sides and Two Angles Are Given

Q. To construct a trapezium ABCD with $AB\parallel CD,$ the following measurements are given:
AB = 5.5 cm, BC = 4.9 cm and $\angle ABC={70}^{\circ }.$
Which other measure will help complete the construction?

1. $\angle DAB$
2. AE, the altitude from the point A onto CD.
3. CM, the altitude from the point C onto AB.
4. We need at least two more measures to uniquely construct this trapezium.

Q. To construct a trapezium ABCD with $AB\parallel CD,$ AB = 6.5 cm, BC = 6.2 cm, $\angle ABC={80}^{\circ }$ and $\angle DAB={105}^{\circ },$ we follow the following steps:
1) Draw the line segment AB = 6.5 cm.
2) Construct the angle $\angle ABX={80}^{\circ }$ at B.
3) With B as centre, draw an arc of radius 6.2 cm cutting BX at C.
4) Draw CD parallel to AB.
The next step involved in the construction is __.

1. Construct the angle $\angle BAZ={105}^{\circ }$ at A cutting CY at D.
2. From the point A, draw an arc of radius 6.2 cm cutting CY.
3. From the point A, draw an arc of radius 6.6 cm cutting CY.
4. Construct the angle $\angle BAZ={75}^{\circ }$ at A cutting CY at D.

Q. Construct a trapezium DEAN in which DE is parallel to NA, DE = 7 cm, EA = 6.5 cm, $\angle$ EDN = 100${}^{\circ }$ and $\angle$ DEA = 70${}^{\circ }$ . Also find its area.

Q. Question 202
Construct a trapezium RISK in which $RI\parallel KS$, RI = 7 cm, IS = 5 cm, RK = 6.5 cm and $\angle I={60}^{\circ }$.

Q. Question 203
Construct a trapezium ABCD, where $AB\parallel CD$, AD = BC = 3.2 cm, AB = 6.4 cm and CD = 9.6 cm. Measure $\angle B$ and $\angle A$.

[Hint Difference of two parallel sides gives an equilateral triangle]

Q. Construct a trapezium DEAN in which DE is parallel to NA, DE = 7 cm, EA = 6.5 cm, $\angle$ EDN = 100${}^{\circ }$ and $\angle$ DEA = 70${}^{\circ }$ . Also find its area.

Q. Question 186
Construct a trapezium ABCD in which $AB\parallel DC,\angle A={105}^{\circ }$, AD = 3 cm, AB = 4 cm and CD = 8 cm.

Q. To construct a trapezium ABCD with $AB\parallel CD,$ AB = 6.5 cm, BC = 6.2 cm, $\angle ABC={80}^{\circ }$ and $\angle DAB={105}^{\circ },$ we follow the following steps:
1) Draw the line segment AB = 6.5 cm.
2) Construct the angle $\angle ABX={80}^{\circ }$ at B.
3) With B as centre, draw an arc of radius 6.2 cm cutting BX at C.
4) Draw CD parallel to AB.
The next step involved in the construction is __.

Q. The area of the trapezium $PQRS$ is approximately:

1. $5.25c{m}^2$
2. $4.2c{m}^2$
3. $8.4c{m}^2$
4. $5.75c{m}^2$