Constructing a Trapezium When Its Three Sides and One Angle Are Given

Q.

Draw the following: A rhombus whose diagonals are $5.2$ cm and $6.4$ cm long.

Q. What is the minimum number of measurements we need to construct a trapezium?

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

Q. To construct a trapezium ABCD with $AB\parallel CD,$ AB = 8 cm, BC = 5 cm, AD = 6 cm and $\angle ABC={60}^{\circ },$ we follow the following steps:
1) Draw the line segment AB = 8 cm.
2) Construct the angle $\angle ABX={60}^{\circ }$ at B.
3) With B as centre, draw an arc of radius 5 cm cutting BX at C.

The next step is ___.

1. Draw CY parallel to AB.
2. Draw a line segment AY parallel to BC.
3. With A as centre, draw an arc of radius 6 cm cutting BX.
4. With B as centre, draw an arc of radius 6 cm cutting BX.

Q. Construct a trapezium BOAT in which $\overline{BO}$ is parallel to $\overline{TA},BO=7cm,OA=6cm,$ $BA=10cm$ and $TA=6cm$. Also find its area.

Q. Construct a trapezium ABCD with dimesions: $AB=6cm,AD=4cm,CD=3cm$, $\angle DAB={90}^o$, and $AB\parallel CD$. Find the area of the trapezium ABCD (in sq. cm).

1. $20$
2. $16$
3. $18$
4. None of these

Q. Construct a trapezium PQRS in which $\overline{PQ}$ is parallel to $\overline{SR}$ , PQ = 8 cm $\angle$ PQR = ${70}^o$, QR = 6 cm and PS = 6 cm. Calculate its area.

Q. The area of a trapezium is $475c{m}^2$ and the height is 19 cm, then the lengths of smaller side of two parallel sides if one side is 4 cm greater than the other is

Q. Construct a trapezium ABCD with dimesions: $AB=6cm,AD=4cm,CD=3cm$, $\angle DAB={90}^o$, and $AB\parallel CD$. Find the value of $\angle BCD$ (in degrees).

1. $127$
2. $107$
3. $160$
4. None of these

Q. Two circles intersect as shown in the diagram below. The radii of the circles are 14cm each and $\angle AOP={45}^{\circ }$​ What is the area of the region shaded in blue?

1. $56sq.cm$
2. $132.5\pi sq.cm$
3. $156sq.cm$
4. $112sq.cm$

Q. How many unique trapeziums can be drawn given three sides and one angle?

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

Q. $l\left(OP\right)=$ ?(in $cm$)

1. $3$
2. $2$
3. $1.5$
4. $4.5$

Q. Construct a trapezium ABCD with dimesions: $AB=6cm,AD=4cm,CD=3cm$, $\angle DAB={90}^o$, and $AB\parallel CD$. What is the value of side BC?

1. $5$cm
2. $6$cm
3. $5.5$cm
4. None of these

Q. Area of the trapezium is:

1. $15.6c{m}^2$
2. $19.5c{m}^2$
3. $9.75c{m}^2$
4. $7.8c{m}^2$

Q. Construct a trapezium ABCD, when :
AB = $4.8$ cm, BC = $6.8$, CD = $5.4$ cm, angle B = ${60}^{\circ }$ and AD || BC.

Q. Construct a trapezium $ABCD$ in which $AD||BC$, $\angle B={60}^o,AB=5cm.BC=6.2cm$ and $CD=4.8cm.$

Q. Construct a trapezium ABCD with dimesions: $AB=6cm,AD=4cm,CD=3cm$, $\angle DAB={90}^o$, and $AB\parallel CD$. Find the value of $\angle ABC$ (in degrees).

1. $53$
2. $60$
3. None of these
4. $37$

Q. Draw the following
A parallelogram $OKAY$ where $OK=5.5cm$ and $KA=4.2cm$. Is it unique?

Q.

To construct rhombus ABCD given CD =5 cm and diagonal BD =8.5 cm, which of the properties of rhombus do we use?

1. Diagonals bisect each other.

2. Diagonals bisect each other at right angles.

3. All sides of a rhombus are equal.

4. Opposite angles are equal.

Q.

If AB = 5 cm, BC = 6 cm, CD = 7 cm, DA = 6 cm and $\angle$ ABC= ${60}^{\circ }$ are given, then can you draw a quadrilateral?

1. Atleast one more measurement is required.

2. Yes

3. No

4. Maybe

Q.

If you are given AB = 5 cm, BC = 6 cm, CD = 7 cm, DA = 6 cm and $\angle ABC$ = ${60}^{\circ }$, then it is possible to draw the quadrilateral ABCD.

1. False

2. True

Q. A pair of opposite sides of a trapezium is ______