Page 14.29

### EXERCISE 14.2

**Type 1**

#### QUESTION 1

**The base and height of a parallelogram are in the ratio of 3:2 and area is 600 sq. metres . Find its base and height**

Sol :

#### QUESTION 2

**The area of a parallelogram is 72cm ^{2} . If its one perpendicular (altitude) is double of the corresponding base , find the base and altitude .**

Sol :

#### QUESTION 3

**Two adjacent sides of a parallelogram ABCD are 5cm and 3.5cm and length of its diagonal is 6.5cm . Find the area of the parallelogram**

Sol :

#### QUESTION 4

**Two adjacent sides of a field which in the shape of a parallelogram are 25m and 39m and one diagonals is 56m , then what will be the cost of laying stone in the field at Rs 3.50 per sq. metre ?**

Sol :

#### QUESTION 5

**Area of a parallelogram ABCD is 120cm ^{2} . If AB=15cm , then find the distance between AB and DC . If ∠CDA=150° , find the perimeter of the parallelogram**

<fig >

<hint>

Sol :

**TYPE 2**

#### QUESTION 6

**Each side of a rhombus is 10m and its one diagonal is 16m , find the area of the rhombus **

Sol :

#### QUESTION 7

**The diagonals of a rhombus are 7m and 24m , then find its**

**(i) area **

**(ii) side**

**(iii) perimeter**

**(iv) height**

Sol :

#### QUESTION 8

**Perimeter of a rhombus is 20cm and its diagonal is 8cm . Find the area of the rhombus and length of other diagonal**

Sol :

#### QUESTION 9

**In figure , (i) OPQR is a rhombus of which three vertices lie on a circle with center O . If area of rhombus be 32√3cm ^{2} , then find the radius of the circle**

<fig>

<hint>

Sol :

#### QUESTION 10

**OABC is a rhombus whose three vertices lie on the circle with centre O . If radius if the circle be 10cm , then find the area of the rhombus**

[Hint: Proceed as in question 9]

Sol :

#### QUESTION 11

**The cross section of canal is trapezium. If width of the upper side is 10m and that of base is 6cm and cross section area of the canal is 72m ^{2 }, find its depth**

<hint>

Sol :

#### QUESTION 12

**Area of a trapezium is 210m ^{2} . If perpendicular distance between the parallel sides is 15m and one of thses parallel sides is 12m , then find its other parallel side**

Sol :

#### QUESTION 13

**The parallel sides of a trapezium are 18 cm and 10 cm. If each of the order two sides is 5cm , then find its area **

Sol :

#### QUESTION 14

**A trapezium PBCQ whose parallel sides QC and PB are in the ratio 7:5 , has been cut from a rectangle ABCD as shown in figure (i) If area of the trapezium is 4/7 of the area of the rectangle ,then find the length of sides QC and PB**

<fig>

<hint>

Sol :

#### QUESTION 15

**Parallel sides of a trapezium are 46 m and 25m and two other sides are 20m and 13m . Find the area of the trapezium**

<fig>

<hint>

Sol :

**TYPE 4**

#### QUESTION 16

**ABCD is a quadrilateral whose diagonal AC=15cm and lengths of perpendiculars drawn from opposite vectors are 3cm and 5cm . Find the area of the quadrilateral**

Sol :

#### QUESTION 17

**The diagonal of a quadrilateral is 50cm and perpendicular drawn to it from opposite vertices are 10cm and 20cm . Find the area of the quadrilateral .**

Sol :

#### QUESTION 18

**Area of a field in the shape of a quadrilateral is 486m ^{2} and its one diagonal is 36m . Perpendiculars drawn from opposite vertices on this diagonal are in the ratio of 4:5 . Find the lengths of the perpendiculars**

<hint>

Sol :

#### QUESTION 19

**Find the area if quadrilateral ABCD whose sides are 5m , 12m , 15m and 14m and angle between first two sides is 90°**

Sol :

#### QUESTION 20

**Find the area of quadrilateral ABCD in which**

**(i) AB=7cm , BC=12cm , CD=12.6cm , DA=9cm and diagonals AC=15cm**

**(ii) AB=3cm , BC=4cm , CD=6cm , DA=5cm and diagonal AC=5cm**

Sol :