## Important Questions for CBSE Class 9 Mathematics Areas of Parallelograms and Triangles

**The topics and sub-topics in NCERT Class 9 Maths Text Book Chapter 12 Heron’s Formula:**

- Heron’s Formula
- Introduction
- Area Of A Triangle – By Heron’s Formula
- Application Of Heron’s Formula In Finding Areas Of Quadrilaterals
- Summary

**IMPORTANT QUESTIONS**

**VERY SHORT ANSWER TYPE QUESTIONS**

**Question.1 Two parallelograms are on equal bases and between the same parallels. Find the ratio of their areas.**

** Solution.** 1:1 [._{.}.Two Parallelograms on the equal based and between the same parallels are equal in area.]

**Question.2 If a triangle and a parallelogram are on same base and between same parallels, then find the ratio of the area of the triangle to the area of parallelogram.**

** Solution.** 1 : 2 [._{.}. If a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is equal to half of the parallelogram.]

**More Resources for CBSE Class 9**

- NCERT Solutions
- NCERT Solutions Class 9 Maths
- NCERT Solutions Class 9 Science
- NCERT Solutions Class 9 Social Science
- NCERT Solutions Class 9 English
- NCERT Solutions Class 9 Hindi
- NCERT Solutions Class 9 Sanskrit
- NCERT Solutions Class 9 IT
- RD Sharma Class 9 Solutions

**Question.3**

**Solution.**

**Question.4.**

**Solution.**

**Question.5**

**Solution.**

**Question.6 In the given figure, D is the mid-point of BC and L mid-is the point of AD. If ar(ΔABL) = x ar(ΔABC), then find the value of x**

** **

** Solution.**

**Question.7**

**Solution.**

**Question.8**

**Solution.**

**Question.9**

**Solution.**

**Question.10**

**Solution.**

**Question.11 In figure, TR ⊥ PS, PQ // TR and PS // QR. If QR = 8 cm, PQ = 3 cm and SP = 12 cm, find arquad. PQRS).[CBSE-14-17DIG1U]**

** Solution.**

**Question.12**

]

**Solution.**

**Question.13**

** Solution.**

**Question.14**

**Solution.**

**SHORT ANSWER QUESTIONS TYPE-I**

**Question.15**

**Solution.**

**Question.16**

**Solution.**

**Question.17 Prove that parallelogram on equal bases and between the same parallels are equal in area. [CBSE March 2012]**

** Solution.**

**Question.18**

**Solution.**

**Question.19**

**Solution.**

**Question.20**

**Solution.**

**Question. 21**

**Solution.**

**Question.22 ABCD is a parallelogram and O is the point of intersection of its diagonals. If ar(ΔAOD) = 4 cm ^{2}, find area of parallelogram ABCD. [CBSE-14-GDQNI3W]**

**Solution.**

**Question.23**

**Solution.**

**Question.24**

**Solution.**

**Question.25**

**Solution.**

**SHORT ANSWER QUESTI-IIONS TYPE**

**Question. 26 A farmer was having a field in the form of a parallelogram PQRS. She took any point A on RS and joined it to points P and Q. In how many parts the field is divided ? What are the shapes of these parts ? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it ?**

** Solution.**

**Question.27**

**Solution.**

**Question.28 InΔPQR, A and B are points on side QR such that they trisect QR. Prove that**

** ar(ΔPQB) = 2ar(ΔPBR).**

** Solution.**

**Question.29 For the given figure, check whether the following statement is true or false. Also justify your answer. PQRS is a trapezium with PQ // SR, PS // RU and ST // II RQ, then ar(PURS) = ar(TQRS)**

** [CBSE-14-ERFKZ8H]**

**Solution.**

**Question.30 In the given figure, WXYZ is a quadrilateral with a point P on side WX. If ZY // WX, show that :**

** (i) ar(ΔZPY) = ar(ΔZXY)**

** (ii)ar(ΔWZY) = ar(ΔAZPY)**

** (iii)ar(ΔZWX) = ar(ΔXWY) [CBSE-14-ERFKZ8H]**

**Solution.**

**Question.31. Triangles ABC and DBC are on the same base BC and A, D on the opposite sides of BC, such that ar(ΔABC) = ar(ΔDBC), show that BC bisect AD.**

** Solution.**

**Question.32 Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that ar(ΔAPB) x ar(ΔCPD) = ar(ΔAPD) X ar(ΔBPC).**

** Solution.**

**Question.33 The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q, then parallelogram PBQR is completed (see figure). Show that ar(({ parallel }^{ gm }ABCD) ) = ar(({ parallel }^{ gm }ABCD) ).**

** [CBSE March 2012]**

**Solution.**

**LONG ANSWER TYPE QUESTIONS**

**Question.34. ΔBCD is a parallelogram and P is any point in its interior. Show that ar(ΔAPB) + ar(ΔCPD)= ar(ΔBPC) + ar(ΔAPD) [CBSE-15-6DWMW5A)**

**Solution.**

**Question.35 In the given figure, ABCD is a square. Side AB is produced to points P and Q in such a way that PA = AB = BQ. Prove that DQ = CP.[CBSE-15-NS72LP7]**

**Solution.**

**Question.36 EFGH is a parallelogram and U and T are points on sides EH and GF respectively. If ar(ΔEHT) = 16 cm ^{2}, find ar(ΔGUF) [CBSE-15-NS72LP7]**

**Solution.**

**Value Based Questions (Solved)**

**Question.1 A farmer having afield in the form of parallelogram PQRS.**

** He planned to built a home for old persons of the village in the field leaving open portion equal to portion covered by the home. For this he divided the field by taking a point A on RS and joining AP, AQ respectively as shown in figure.**

** (i) How should he do it ?**

** (ii)What values are depicted in his plan ?**

**Solution.**

**Question.2 Naveen was having a plot in the shape of a quadrilateral. He decided to donate some portion of it to construct a home for orphan girls. Further he decided to buy a land in lieu of his donated portion of his plot so as to form a triangle.**

** (i) Explain how this proposal will be implemented ?**

** (ii)Which mathematical concept is used in it ?**

** (iii)What values are depicted by Naveen ?**

** Solution.**

(ii) Area of parallelogram and triangle and mid-point theorem.

(iii) Every child, boy or girl have equal right, so avoid discrimination in boy and girl.

**Question.3 Mr Sharma explains his four children two boys and two girls about distribution of his property among them by a picture of A ABC such that D, E, F are mid-points of sides AB, BC, CA respectively are joined to divide A ABC in four triangles as shown in figure.**

** (i) If total property is equal to area of A ABC and share of each child is equal to area of each of four triangles, what does each child has share ?**

** (ii)Which mathematical concept is used in it ?**

** (iii)Which values are depicted in Mr Sharma’s plan ?**

**Solution.**

**Question.4 A flood relief camp was organized by state government for the people affected by the natural calamity near a city. Many school students volunteered to participate in the relief work. In the camp, the food items and first aid centre kits were arranged for the flood victims.**

** The piece of land used for this purpose is shown in the figure.**

** (a) If EFGH is a parallelogram with P and Q as mid-points of sides GH and EF respectively, then show that area used for first aid is half of the total area.**

** (b) What can you say about the student volunteers working for the relief work ?**

** [CBSE-14-GDQNI3W]**

** Solution.**

**Question.5 Sunita has a plot of land which she decides to use for building an old age home and a dispensary for the needy. Her plot is shown in the figure. Plot ABCD is a parallelogram**

** (a) If R is point on diagonals BD. Show that equal areas allotted for building old age home and the dispensary.**

** (b) What value is depicted by the above situation ?**

**Solution.**

## NCERT Solutions for Class 9 Maths

- Chapter 1 Number systems
- Chapter 2 Polynomials
- Chapter 3 Coordinate Geometry
- Chapter 4 Linear Equations in Two Variables
- Chapter 5 Introduction to Euclid Geometry
- Chapter 6 Lines and Angles
- Chapter 7 Triangles
- Chapter 8 Quadrilaterals
- Chapter 9 Areas of Parallelograms and Triangles
- Chapter 10 Circles
- Chapter 11 Constructions
- Chapter 12 Heron’s Formula
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability
- Class 9 Maths (Download PDF)