NCERT Class 9 Maths Areas Of Parallelograms And Triangles

9.1 Introduction

In Chapter 5, you have seen that the study of Geometry, originated with the measurement of earth (lands) in the process of recasting boundaries of the fields and dividing them into appropriate parts. For example, a farmer Budhia had a triangular field and she wanted to divide it equally among her two daughters and one son. Without actually calculating the area of the field, she just divided one side of the triangular field into three equal parts and joined the two points of division to the opposite vertex. In this way, the field was divided into three parts and she gave one part to each of her children. Do you think that all the three parts so obtained by her were, in fact, equal in area? To get answers to this type of questions and other related problems, there is a need to have a relook at areas of plane figures, which you have already studied in earlier classes.

You may recall that the part of the plane enclosed by a simple closed figure is called a planar region corresponding to that figure. The magnitude or measure of this planar region is called its area. This magnitude or measure is always expressed with the help of a number (in some unit) such as 5 cm², 8 m², 3 hectares etc. So, we can say that area of a figure is a number (in some unit) associated with the part of the plane enclosed by the figure.

We are also familiar with the concept of congruent figures from earlier classes and from Chapter 7. Two figures are called congruent, if they have the same shape and the same size. In other words, if two figures A and B are congruent (see Fig. 9.1) , then using a tracing paper,

Question. In the pattern below, each smaller triangle is formed by joining the midpoints of the triangle immediately larger than it.  
What part of triangle PQR is shaded?

A. 3/5
B. 13/16
C. 49/64
D. 51/64

Answer : D

Question. If all the white squares that touch the border of the board below are cut out, what will  happen to the perimeter of the remaining piece as compared to that of the original board?

A. it will increase by 16 units
B. it will increase by 8 units
C. it will decrease by 8 units
D. it will remain the same

Answer : B

Question. Which two parallelograms are equal in area?

A. PQRS and PQXY
B. PQRS and PQVW
C. PQTU and PQVW
D. Cannot be decided

Answer : D

Question. A square of side 10cm has triangle inscribed in it as shown. what is the of triangle PQR?

A. 45 cm²
B. 50 cm²
C. 25√3 cm²
D. Can't say without knowing the position of Q

Answer : B

Question. For a right-angled isosceles triangle , the ratio of the length of hypotenuse to the length of any of its smaller side 
A. Is always fixed and equal to √2 :1
B. Is always fixed and equal to 1:1
C. Is always fixed and equal to 2:1
D. Varies with the change in the length of its other sides.

Answer : A

Question. If represents 75%,which of the following represents125%

Answer : C

Question. Leslie and Surekha were standing on opposite sides of a road. Suddenly, they spotted a puppy stranded on the road and both rushed straight to where the puppy was, to pick it up. If Leslie ran at an angle of 350 to the edge of the road and Surekha at an angle of 〖70〗^oat what angle did their paths meet?

A. 75⁰
B. 105⁰
C. 135⁰
D. 145⁰

Answer : D

Question. What is the measure of the angle marked 'q' in the figure?

A. 45⁰
B. 67.5⁰
C. 135⁰
D. 70⁰

Answer : D

Question. A square is cut in half to form two equal rectangles. If each of the two resulting rectangles has a perimeter of p cm, what was the perimeter (in cm) of the original square?
A. 2p
B. (2/3)p
C. 3p
D. (4/3)p

Answer : D

Question. In quadrilateral ABCD, ∠ A + ∠B= ∠ C + ∠D = 180^∘. But ∠A≠ ∠C.Quadrilateral ABCD must be a
A. Rectangle
B. Parallelogram
C. Rhombus
D. Trapezium

Answer : D

Question. MNOP is a quadrilateral with M:  N:  O:  P = 2:2:1:1 and MN and OP ae opposite sides ,what kind of quadrilateral is MNOP 
A. A rectangle
B. A rhombus
C. A trapezium
D. A parallelogram

Answer : C

Question. If four shapes - a square, a rectangle, a triangle and a circle - have the same area, which of them will have the smallest perimeter?
A. the triangle
B. the square
C. the rectangle
D. the circle

Answer : D

Question. What is the measure of the smaller angle in the rhombus shown in the image?

A. 108⁰
B. 72⁰
C. 58⁰
D. 22⁰

Answer : B

Question. In which case will the pair of triangles DEFINITELY be congruent? (Figures not to scale - consider only measures given)

Answer : C
 

Please refer to attached file for NCERT Class 9 Maths Areas Of Parallelograms And Triangles