Knowing & Measuring Triangles

Mensuration on Triangles

A triangle is a closed figure formed by three line segments.  It has three vertices, three sides and three angles. 

In any triangle drawn by joining three non-collinear points, the sum of the lengths of any two sides is greater than the length of the third side. This property is called as Triangle inequality.  

Few important points about triangles:

1. Triangle is formed by joining three ______________ points.

2. A triangle has ______________ vertices and ______________ sides.

3. A point where two sides of a triangle meet is known as ________ of a triangle.

4. Each angle of an equilateral triangle is of ______________ measure.

5. A triangle has angle measurements of 29°, 65° and 86°. Then it is _______ triangle.

(i) an acute angled                   (ii) a right angled
(iii) an obtuse angled               (iv) a scalene

6. A triangle has angle measurements of 30°, 30° and 120°. Then it is _______ triangle.

(i) an acute angled                   (ii) scalene
(iii) obtuse angled                   (iv) right angled

7. Which of the following can be the sides of a triangle?

(i) 5,9,14          (ii) 7,7,15         (iii) 1, 2, 4        (iv) 3, 6, 8

8. Ezhil wants to fence his triangular garden. If two of the sides measure 8 feet and 14 feet then the length of the third side is __________

(i) 11 ft            (ii) 6 ft             (iii) 5 ft            (iv) 22 ft

9. Can we have more than one right angle in a triangle?

10. How many obtuse angles are possible in a triangle?

11. In a right triangle, what will be the sum of other two angles?

12. Is it possible to form an isosceles right angled triangle? Explain.

Test Your Knowledge on Triangles

MCQ on Exponents and Powers (Grade 7)

Multiple Choice Questions

EXPONENTS AND POWERS

1.  Fill in the blanks.

(i) The exponential form 14⁹ should be read as_______________

(ii)  The expanded form of p³q² is________________

(iii)  When base is 12 and exponent is 17, its exponential form is_____________

(iv) The value of (14 × 21)⁰  is_______________

2.  Say True or False.

(i) 2³ × 3² = 6⁵

(ii)  2⁹ × 3² =   (2 × 3)^9×2

(iii)  3⁴ × 3⁷ = 3¹¹

(iv)  (2)⁰ = (1000)⁰

(v) 2³ < 3²

3. a×a×a×a×a  is equal to
(i) a⁵                (ii) 5^a               (iii) 5a             (iv) a+5

4. The exponential form of 72 is
(i)7²                 (ii) 2⁷               (iii) 2² × 3³       (iv) 2³ × 3²  

5. The value of x in the equation a¹³ = x³ × a¹⁰ is
(i) a                  (ii) 13               (iii) 3                (iv) 10

6. How many zeros are there in 100¹⁰? 

(i) 2                 (ii) 3                 (iii) 10             (iv) 20

7. 2⁴⁰ + 2⁴⁰ is equal to
(i) 4⁴⁰             (ii) 2⁸⁰             (iii) 2⁴¹             (iv) 4⁸⁰

8.  Fill in the blanks.
(i) The degree of the term a³b²c⁴d² is ___________.
(ii)  Degree of the constant term is ______.
(iii)  The coefficient of leading term of the expression  3z²y + 3x − 2  is _________. 

9.  Say True or False:
(i) The degree of m²n and mn² are equal.
(ii) 7a²b and −7ab² are like terms.
(iii) The degree of the expression −4x²yz is −4.

10.  3p² − 5pq + 2q² + 6 pq − q² + pq   is a
(i) Monomial               (ii) Binomial
(iii) Trinomial             (iv) Quadrinomial

11.  The degree of 6x⁷ – 7x³ + 4 is
(i) 7                  (ii) 3                 (iii) 6                (iv) 4

12. If p(x)  and q(x)  are two expressions of degree 3, then the degree of p(x)  + q(x)  is
(i) 6                  (ii) 0                 (iii) 3                (iv) Undefined

13.

(i) 3⁶⁺⁴⁺¹⁰                      (ii) 3^6x4x10                    
(iii) 3^6-4+10                    (iv) 3^(6-4)x10

14. The correct value of (3²)³
(i) 18                            (ii) 216            
(iii) 729                        (iv) 243

15. The value of 7^(-2)
(i) -49                         (ii) 49  
(iii) 1/49                       (iv) -14

16. 3⁶ x 2³ x 4² x 3⁰ ÷ 3⁴ x 2⁵ x 2²
(i) 9                  (ii) 4                 (iii) 1                (iv) 1/8

17. 864000000 can be written in scientific notation as
(i) 8.64 x 10⁶               (ii) 8.64 x 10⁷                         
(iii) 8.64 x 10¹⁰            (iv) 8.64 x 10⁸

18. 0.0000952 can be written in scientific notation as
(i) 9.52 x 10^(-7)             (ii) 952 x 10⁷              
(iii) 9.52 x 10^(-5)           (iv) (0.952 x 10)^-12

19. 1 ÷ 81 is not equal to
(i) 1 ÷ 3⁴                      (ii) (1÷3)⁴        
(iii) (1÷3)^-1                   (iv) (3)^-4

^Answers:

^{1.  (i)     14 raised to the power 9
    (ii)    p x p x p x q x q
    (iii)}   12¹⁷

2.   (i) False     (ii) False          (iii) True
      (iv) True         (v) True

3.   (i) a⁵

4.   (iv) 2³ × 3²

5.   (i) a

6.   (iv) 20

7.   (i) 4⁴⁰

8.   (i) 4                        (ii) 0                 (iii) 3

9.   (i) True                   (ii) False          (iii) True 

10.

                        (or)

11.  (i) 7

12. (iii) 3

13.  (iv) 3^(6-4)x10

   

14.  (iii) 729

    (3²)³ = 3^2x3= 3⁶ = 729

15.  (iii) 1/49

16.  (i) 9

17.  (iv) 8.64 x 10⁸

18.  (iii) 9.52 x 10^(-5)

19.  (iii) (1÷3)^-1

MCQ on Measuring Circles (Grade 7)

 Multiple Choice Questions

MEASUREMENT ON CIRCLES

1. Formula used to find the circumference of a circle is 

(i) 2πr units                  (ii) πr² + 2 r units
(iii)πr² sq. units            (iv) πr3 cu. units

2.  In the formula, C = 2πr, ‘r’ refers to

(i) circumference               (ii) area
(iii) rotation                       (iv) radius

3.  If the circumference of a circle is 82π, then the value of ‘r’ is

(i) 41 cm                      (i5i) 82 cm
(iii) 21 cm                    (iv) 20 cm

4. Circumference of a circle is always

(i) three times of its diameter
(ii)  more than three times of its diameter
(iii) less than three times of its diameter
(iv) three times of its radius

5. The formula used to find the area of the circle is  sq. units.

(i) 4 πr²                        (ii) πr²
(iii) 2 πr²                      (iv)  πr² + 2r.

6. The ratio of the area of a circle to the area of its semicircle is

(i) 2:1               (ii) 1:2             (iii) 4:1             (iv) 1:4 

7.  Area of a circle of radius ‘n’ units is

(i) 2πr^p sq. units           (ii) πm² sq. units
(iii) πr² sq. units           (iv) πn² sq. units

8. The formula to find the area of the circular path is

(i) π (R² − r²) sq. units           (ii) πr² sq. units 
(iii) 2πr² sq. units         (iv)  πr² + 2r sq. units

9. The formula used to find the area of the rectangular path is

(i) π (R² − r²) sq. units   

(ii) (L × B) − ( l × b)  sq. units   

(iii) LB sq. units                      

(iv) lb sq. units

10. The formula to find the width of the circular path is

(i) (L − l) units             (ii) (B − b) units
(iii) (R − r) units          (iv) (r − R) units

11. Which term is used to represent the perimeter of a circle?

(i) Radius                    (ii) Diameter
(iii) Circumference    (iv) Chord

12. If the diameter of a circle is 20 cm, the length of its circumference is

(i) 11π cm        (ii) 20π cm       (iii) 40π cm      (iv) 80π cm

13. If the circumference of a circle is 16π, its area is

(i) 8π                (ii) 16π             (iii) 32π            (iv) 64π

14. What is the area of the shaded part?

(i) 81π sq. m.               (ii) 49π sq. m.
(iii) 4π sq. m.               (iv) 32π sq. m.

Answers to MCQs: 

1.  (i) 2πr units 

2.  (iv) radius

3.

  

4.

5.  (ii) πr²

6.  (i) 2:1

7.  (iv) πn² sq. units

8.  (i) π (R² − r²) sq. units

9.  (ii) (L × B) − ( l × b)  sq. units

10.  (iii) (R − r) units

11.  (iii) Circumference

12.  

13.

14.

MCQ on Number System (Grade 7)

 Multiple Choice Questions

Number System

Q 1)The place value of 3 in 85.073 is _______ 

(i) tenths     (ii) hundredths      (iii) thousands     (iv) thousandths 

Q 2) To convert grams into kilograms, we have to divide it by 

(i) 10000         (ii) 1000         (iii) 100         (iv) 10

Q 3) The decimal representation of 30 kg and 43 g is ____ kg. 

(i) 30.43         (ii) 30.430         (iii) 30.043          (iv) 30.0043 

Q 4) A cricket pitch is about 264 cm wide.  It is equal to ____ m. 

(i) 26.4         (ii) 2.64         (iii) 0.264         (iv) 0.0264 

Q 5 to 7

8 to 10

11.  Between which two whole numbers 1.7 lie? 

(i)  2 and 3         (ii) 3 and 4         (iii) 1 and 2         (iv) 1 and 7

12. The decimal number which lies between 4 and 5 is ____ 

(i) 4.5             (ii)  2.9                 (iii)  1.9                 (iv)  3.5 

13.  In the number 2.007, what is the place value of 7?

(i) tenths     (ii) hundredths      (iii) thousands     (iv) thousandths

14.  In the number 70.100, what is the place value of 1?

(i) tenths     (ii) hundredths      (iii) thousands     (iv) thousandths

15.  What is the place value of 3 in 5.0360?

(i) tenths     (ii) hundredths      (iii) thousands     (iv) thousandths

16.  What is the place value of 4 in 9.0004?

(i) tenths     (ii) hundredths      (iii) thousandths     (iv) ten-thousandths

17.  What is the value of 0.2 + 0.2?

(i) 0.2     (ii) 0.04      (iii) 0.4     (iv) 4

18.  0.2 / 0.2?

(i) 0.1     (ii) 0.01      (iii) 2     (iv) 1

Summary:

Answers to MCQ on Number System:

1. (ii) Hundredths

2. (ii) 1000

3.

4.  (ii) 2.64

5.

6. (iv) 0.6

7.

8.  (iii) 0.00900

9.  (i) =

10.  (i) <

11.  (iii) 1 and 2

12.  (i) 4.5

13.  (iv) thousandths

14.  (i) tenths

15.  (ii) hundredths

16.  (iv) ten-thousandths

17.  (iii) 0.4

18.  (iv) 1

Problems on Square, Rectangle and Circle

Problems to Solve on Mensuration

1.      Find the perimeter of the following rectangles.

a.       Rectangle ABCD in which AB = 20 cm, BC = 15 cm.

b.      Rectangle PQRS in which PQ = 18 cm, QR = 12 cm.

2.      Kayla wants to build a fence in her backyard. The length of her backyard is 30 feet and the width is 45 feet. How many feet of fence will she need to buy?

3.      The area of a soccer field is 56 square yards. The length of one side of the field is 8 yards. What is the width of the field?

4.      Farmer John walks his pet pig around his barn every day. The barn is 25 meters by 12 meters. If he makes the pig walk around the barn three times, how many meters did farmer John and his pig walk?

5.      If the area of a basketball court in 117 square feet and the width is 9 feet, what is the length?

6.       Jenny's room is 13 feet long and 12 feet wide. Ruth's room is 14 feet long and 11 feet wide. Whose room has the greater perimeter?

7.      Stephen has a rectangular bedroom with a perimeter of 34 feet. The length of the bedroom is 9 feet. What is the width of Stephen's bedroom?

8.      A living room wall is 20 feet long, and 12 feet high. How much paint do you need to cover one wall?

9.       If a rectangle is 9 cm by 2 cm, what is its perimeter?  What is its area?  

10.  Penny's garden has a fountain in the middle that has a base of 5 in. and the height is 9 in. The garden around it has a base of 16 in. and the height is 5 in. What is the area of the garden excluding the fountain?

11.  The length and the breadth of a rectangular piece of land are 500 m and 300 m respectively. Find its area.

12.  Find the breadth of a rectangular plot of land, if its area is 440 m² and the length is 22 m. Also find its perimeter.

13.  The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area.

14.  The area of a square park is the same as of a rectangular park.  If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.

15.  A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm.  If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area?

16.  The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is 30 cm, find its length. Also find the area of the rectangle.

17.  A door of length 2m and breadth  1m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m. Find the cost of white washing the wall, if the rate of white washing the wall is Rs. 20 per m².

18.  Kannan divides a circular disc of radius 14 cm into four equal parts.  What is the perimeter of a quadrant shaped disc?

19.  A Rose garden is in the form of circle of radius 63 m.  The gardener wants to fence it at the rate of ₹150 per metre.  Find the cost of fencing?

20.  A wire of length 1320 cm is made into circular frames of radius 7 cm each. How many frames can be made?

Points to Remember:

1.       Perimeter is the distance around a closed figure whereas area is the part of plane occupied by the closed figure.

2.      Formula to find perimeter and area of a square and rectangle are as follows:

a.       Perimeter of a square = 4 × side

b.      Perimeter of a rectangle = 2 × (length + breadth)

c.       Area of a square = side × side

d.      Area of a rectangle = length × breadth

3.      The distance around a circular region is known as its circumference.

a.       Circumference of a circle = πd, where d is the diameter of a circle and π = 22/7 or 3.14 (approximately).

b.      Area of a circle = πr², where r is the radius of the circle.

Answers:

1.               a. 70 cm
b. 60 cm