Perimeter and Area of Trapezium

Q.

The area of a trapezium is 180 $c{m}^2$ and its height is 9 cm. If one the parallel sides is longer than the other by 6 cm, the length of the longer of the parallel sides is
(a) 17 cm (b) 23 cm
(c) 18 cm (d) 24 cm

Q.

Find the area of a trapezium whose parallel sides are $24cm$ and $20cm$ and the distance between them is $15cm.$

Q.

The area of a trapezium is 405 $c{m}^2$. Its parallel sides are in the ratio 4 : 5 and the distance between them is 18 cm. Find the length of each of the parallel sides.

Q.

Every quadrilateral has two pairs of parallel sides.

1. True

2. False

Q.

Find the area of given figure $ABCDEFGH$ as per dimensions given in it.

Q.

Find the area of the trapezium ABCD in which AB//DC, AB =18 cm, $\angle B=\angle C={90}^{\circ },CD=12$ cm and AD =10 cm.

Q.

The lengths of the parallel sides of a trapezium are 19 cm and 13 cm and its area is 128 $c{m}^2$. The distance between the parallel sides is
(a) 9 cm (b) 7 cm
(c) 8 cm (d) 12.5 cm

Q.

The parallel sides of a trapezium measure 14 cm and 18 cm and the distance between them is 9 cm. The area of the trapezium is
(a) $96c{m}^2$ (b) $144c{m}^2$
(c) $189c{m}^2$ (d) $207c{m}^2$

Q. If the length of a side of a rectangle is 12 cm and its diagonal is 13 cm, find its area.

1. 60 $c{m}^2$
2. 156 $c{m}^2$
3. 26 $c{m}^2$
4. 30 $c{m}^2$

Q.

The parallel sides of a trapeziuim are in the ratio 3:4 and the perpendicular distance between them is 12 cm. If the area of the trapezium is 630 $c{m}^2$, then its shorter of the parallel sides is
(a) 45 cm (b) 42 cm
(c) 60 cm (d) 36 cm

Q.

The following figure shows the cross-section ABCD of a swimming pool which is trapezium in shape.

If the width DC, of the swimming pool is 6.4 cm, depth (AD) at the shallow end is 80 cm and depth (BC) at deepest end is 2.4 m, find Its area of the cross-section.

Q. Which of the following statements is incorrect?
(A) Every parallelogram is a quadrilateral.
(B) Every rectangle is a parallelogram.
(C) Every square is a rectangle.
(D) Every trapezium is a parallelogram.

1. A
2. B
3. C
4. D

Q.

The area of a trapezium is 279 sq. cm and the distance between its two parallel sides is 18 cm. If one of its parallel sides Is longer than the other side by 5 cm, find the lengths of its parallel sides.

Q.

A field is in the shape of a quadrilateral ABCD in which side AB =18 m, side AD=24 m, side BC =40 m, DC =50 m and angle $A={90}^{\circ }$. Find the area of the field.

Q.

Draw a quadrilateral with equal diagonals, which is not a rectangle.

Q.

The two parallel sides and the distance between them are in the ratio 3 : 4 : 2. If the area of the trapezium is 175 cm2; find its height.

Q.

An isosceles trapezium has an area of $36c{m}^2$, the parallel sides are $12cm$ and $6cm$ respectively. The perimeter of the trapezium is

1. 28 cm

2. 32 cm

3. 24 cm

4. 20 cm

Q.

The shape of the top surface of a table is trapezium. Its parallel are sides are 1 m and 1.4 m and the perpendicular distance between them is 0.9 m. Find its area.

Q. In a trapezoid ABCD, the diagonals intersect at E.If area of triangle ABE=72 and area of triangle CDE=50, then area of trapezium ABCD is ?

Q.

The parallel sides of an isosceles trapezium are in the ratio $2:3$. If its height is $8cm$ and area is $240c{m}^2$, then its perimeter is ____ cm.

1. 96

2. 100

3. 60

4. 80

Q.

Tho parallel sides of a trapezium are in the ratio 3 : 4. If the distance between the parallel sides Is 9 dm and its area is $126d{m}^2$, find the lengths of its parallel sides.

Q. A balcony attached to a building is in the shape of trapezium.The side not attached to the building is parallel to and double the side attached to the building. If the area of the balcony is 18m square and the distance between the two parallel sides is 9m find the length of the side of the balcony not attached to the building.

Q. ABCD is a quadrilateral in which diagonal BD is perpendicular to the side AB. If AB=4.5 cm, AD=7.5 cm and the dis†an ce of C from BD is 1.5 cm, then find the area of quadrilateral

Q.

A quadrilateral has an area of $453.6m^2$. The length of a diagonal is 42 m and the perpendicular distance from one vertex to the diagonal is 10 m. The perpendicular distance from the other vertex to the diagonal is ___ .

Q.

The perimeter of a trapezium is $52cm$ and its each non parallel side is equal to $10cm$ with its height $8cm.$Its area is

1. $124c{m}^2$

2. $118c{m}^2$

3. $128c{m}^2$

4. $112c{m}^2$

Q.

Are all re parallelograms trapeziums?

Are all squares trapizitra

Q.

A quadrilateral has an area of 453.6m². The length of a diagonal is 42 m and the perpendicular distance from one vertex is 10 m. The perpendicular distance from the other vertex is __

Q. Find the cube root of $-3375$.

1. $-25$
2. $-15$
3. Not defined
   
4. None of these
   

Q. Which of the following statements is incorrect?
(A) Every parallelogram is a quadrilateral.
(B) Every rectangle is a parallelogram.
(C) Every square is a rectangle.
(D) Every trapezium is a parallelogram.

1. B
2. D
3. A
4. C

Q. The parallel sides of a trapezium are $x$ and $y$ in length. The length of the line segment joining the mid points of the non parallel sides is:

1. $\frac{x+y}{2}$
2. $x+y$
3. $\frac{2x+3y}{2}$
4. $\frac{xy}{2}$