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**Frank Learning Maths Class 6 Solutions Chapter 12 Understanding Elementary Shapes**

Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Frank Learning Maths Class 6 Book, Chapter 12 Understanding Elementary Shapes. Here students can easily find step by step solutions of all the problems for Understanding Elementary Shapes. Here students will find solutions for Exercise 12.1, 12.2, 12.3, 12.4, 12.5, 12.6 and 12.7. Exercise wise proper solutions. All the problem are solved with easily understandable methods so that all the students can understand easily. Here in this post all Mathematic solutions are based on the CBSE latest curriculum.

**Understanding Elementary Shapes Exercise 12.1 Solution**

**Question no – (1) **

**Solution : **

We can’t compare precisely two line segments if their lengths are almost same.

**Question no – (2) **

**Solution : **

Measuring with divider is better.

Because wrong positioning of eye doesn’t affect here.

**Question no – (4) **

**Solution : **

Yes, we generalize this result for any line segment.

**Question no – (5) **

**Solution : **

= B does not lie between A and C

= CA + B = CB, A Lies between C and B

**Question no – (6) **

**Solution : **

No, M is not.

**∴** Length of JN

= (4 – 0)

= 4 units = JN = NR

**∴** Length of NR

= (8 – 4)

= 4 units

**Question no – (7) **

**Solution : **

Since, B is the midpoint of AC = AB = BC

Since, C is the midpoint of BD = BC = CD

AB = BC = CD

And, AB + BC + CD = AD

or, AB + AB + AB = AD

or, 3 AB = AD

= AB = 1/3 AD = BC = D

**Question no – (8) **

**Solution : **

**Triangle :**

**(a) the sum of any two sides is greater than the 3rd side.**

= 2.8 + 3.2 = 6> 3.6

= 1 + 2.5 = 3.5 > 3

= 3 + 4 = 7 > 5;

= 2 + 2 = 4 > 2

= 12 + 5 = 17 > 13

**(b) the difference of any two sides is less than the 3 rd side.**

= 3.6 – 3.2 = 0.4 < 2.8

= 3 – 1 = 2 < 2.5;

= 5 – 3 = 2 < 4

= 2 – 2 = 0 < 0

= 13 – 5 = 8 < 12

**Question no – (9) **

**Solution : **

Figure – **(a)** AB = BC = CA

Figure – **(b)** BC = AC

Figure – **(c)** SR = SP = PQ = PQ

Figure – **(d)** WX = XY, WZ = XY

**Question no – (10) **

**Solution : **

The lengths of the given line segments in the descending order,

= AB, YZ, ST, UV, WX

**Understanding Elementary Shapes Exercise 12.2 Solution**

**Question no – (1) **

**Solution : **

The vertex and arms of the given angles :

In figure – **(a)** Vertex = O, Arms = OA, OB

In figure **– (b)** Vertex = Q, Arms = PQ, QR

In figure **– (c)** Vertex = D, Arms = DE, DC

**Question no – (2) **

**Solution : **

In the given adjoining figure there are Six angles.

Name of the six angles are,

= ∠DOC, ∠DOB ∠DOA, ∠COB, ∠COA, ∠BOA

**Question no – (3) **

**Solution : **

**(a) 12 to 3**

= 90°/360°

= 1/4

**(b) 4 to 7**

= 90°/360°

= 1/4

**(c) 3 to 9**

= 90°/360°

= 1/4

**(d) 1 to 10**

= 300°/360°

= 5/6

**Question no – (4) **

**Solution : **

**(a)** if you stand facing east and turn clockwise to face south, then you have turned through 90° part of a revolution.

**(b)** If you stand facing west and turn anticlockwise to face north, then you have turned through 270° part of a revolution.

**(c)** If you stand facing north and turn clockwise to face south, then you have turned through 180° part of a revolution.

**(d)** If you stand facing north and turn anticlockwise to face east, then you have turned through North part of a revolution.

**Question no – (5) **

**Solution : **

**(a)** If you stand facing north and make 1/2 of a revolution anticlockwise, then, you will face South direction.

**(b)** If you stand facing east and make one full revolution, then, you will face East direction.

**(c)** If you stand facing east and make 3/4 of a revolution clockwise. then, you will face North direction.

**(d)** If you stand facing west and make 1 1/2 of a revolution anticlockwise. then, you will face North direction.

**Question no – (6) **

**Solution : **

**(a)** If hour hand of a clock starts at 3 and makes 1/2 of a revolution, then it will stop at 9.

**(b)** If hour hand of a clock starts at 4 and makes 1/4 of a revolution, then it will stop at 7

**(c)** If hour hand of a clock starts at 7 and makes 1/4 of a revolution, then it will stop at 1.

**(d)** If hour hand of a clock starts at 5 and makes 3/4 of a revolution, then it will stop at 2.

**Question no – (7)**

**Solution : **

**(a) 1 to 4**

= only 1 right angle is formed by the hour hand of a clock when it moves from 1 to 4.

**(b) 12 to 3**

= 1 only 1 right angle is formed by the hour hand of a clock when it moves from 12 to 3.

**(c) 3 to 9**

= 2 right angles are formed by the hour hand of a clock when it moves from 3 to 9.

**(d) 12 to 6**

= 2 right angles are formed by the hour hand of a clock when it moves from 12 to 6.

**Question no – (8) **

**Solution : **

In each full turn, it turns 4 right angles

Therefore,

In 5 and half turns it will turn

= (4 × 5) + 2

= 22 right angles.

**Question no – (9) **

**Solution : **

**(a)** East direction you will face if you turn to right through One right angle

**(b)** South direction you will face if you turn to right through One straight angle.

**(c)** West direction you will face if you turn to right through three right angles.

**Question no – (10) **

**Solution : **

**(a)** If you start facing south and turn clockwise to west, then you make only one 1 right angle.

**(b)** If you start facing north and turn anticlockwise to east, then you make 3 right angles.

**(c)** If you start facing west and turn to west, then you make 4 right angles.

**(d)** If you start facing south and turn to north, then you make 2 right angles.

**Question no – (11) **

**Solution : **

**(a)** If hour hand of a clock starts from 6 and turns through 1 right angle, then it will stop at 9.

**(b)** If hour hand of a clock starts from 8 and turns through 2 right angles, then it will stop at 2.

**(c)** If hour hand of a clock starts from 10 and turns through 3 right angles, then it will stop at 7.

**(d)** If hour hand of a clock starts from 7 and turns through 2 straight angles, then it will stop at 7.

**Understanding Elementary Shapes Exercise 12.3 Solution**

**Question no – (1) **

**Solution : **

**(a)** Half of a revolution,

= Straight angle

**(b)** The complete revolution,

= Complete angle

**(c)** More than half revolution but less than complete revolution,

= Reflex angle

**(d)** Three-fourth of a revolution,

= Reflex angle

**(e)** Between 1/4 and 1/2 of a revolution,

= Obtuse angle

**Question no – (2) **

**Solution : **

Figure – **(a)** Acute angle.

Figure – **(b)** Right angle.

Figure – **(c)** Acute angle.

Figure – **(d)** Right angle.

Figure – **(e)** Right angle.

Figure – **(f)** Straight angle.

Figure – **(g)** Complete angle.

Figure – **(h)** Reflex angle.

**Question no – (3) **

**Solution : **

**(a)** West and south

= Right angles

**(b)** East and north

= Right angles

**(c)** North and north-east

= Acute angles

**(d)** North and South-west

= Reflex angles

**(e)** North-west and South –east

= Straight angles

**(f)** East and west

= Straight angles

**(g)** South and south-west

= Acute angles

**Question no – (4) **

**Solution : **

**(a)** a right angle

= North-east

**(b)** a straight angle

= South-west

**(c)** a complete angle

= North-west

**Question no – (5) **

**Solution : **

**(a)** 1 revolution = 360°

**(b)** 1/2 revolution = 180°

**(c)** 1/4 revolution = 90°

**(d)** 3/4 revolution = 270°

**(e)** 1 right angle = 90°

**(f)** 2 right angles = 180°

**(g)** 1 straight angle = 180°

**Question no – (6) **

**Solution : **

Acute = 40°, 75°, 55°

Obtuse = 120°, 145°, 135

Reflex = 190°, 225° 210

**Question no – (7) **

**Solution : **

Figure – **(a)** 0°

Figure – **(b)** 30°

Figure – **(c)** 150°

Figure – **(d)** 90°

Figure – **(e)** 180°

Figure – **(f)** 120°

Figure – **(g)** 60°

**Question no – (8) **

**Solution : **

Figure – **(i)** ∠d = obtuse

Figure – **(ii)** ∠e = Acute

Figure – **(iii)** ∠C = right

Figure – **(iv)** ∠G = acute

Figure – **(v)** ∠I = Obtuse

Figure – **(vi)** ∠J = Acute

= H = Acute, ∠K = RIGHT ANGLE.

**Question no – (9) **

**Solution : **

Figure – **(a)** x° + 40° = 180

= x° = 180° – 40°

= 140°

Figure – **(b)** x° = 180° – 60°

= 120°

Figure – **(c)** x° = 180° – 70°

= 110°

Figure – **(d)** x° = 180° – 110°

= 70°

**Question no – (10) **

**Solution : **

**Figure – (a)**

= 90° – 20°

= 70°

**Figure – (b)**

= b° = 90° – 41°

= 49°

**Question no – (11) **

**Solution : **

No, the measure of an angle does not change if we view it through a magnifying glass.

**Understanding Elementary Shapes Exercise 12.4 Solution**

**Question no – (1) **

**Solution :**

**(a)** 1 revolution = 360°

**(b)** 1/2 revolution = 180°

**(c)** 1/4 revolution = 90°

**(d)** 3/4 revolution = 270°

**(e)** 1 right angle = 90°

**(f)** 2 right angles = 180°

**(g)** 1 straight angle = 180°

**Question no – (2) **

**Solution : **

(i) Acute = 40°, 75°, 55°

(ii) Obtuse = 120°, 145°, 135

(iii) Reflex = 190°, 225° 210

**Question no – (3) **

**Solution : **

Figure – **(a)** 0°

Figure – **(b)** 30°

Figure – **(c)** 150°

Figure – **(d)** 90°

Figure – **(e)** 180°

Figure – **(f)** 120°

Figure – **(g)** 60°

**Question no – (4) **

**Solution : **

Figure – **(i)** ∠d = obtuse

Figure – **(ii)** ∠e = Acute

Figure – **(iii)** ∠C = right

Figure – **(iv)** ∠G = acute

Figure – **(v)** ∠I = Obtuse

Figure – **(vi)** ∠J = Acute

**(b)**

∠H = Acute,

∠K = RIGHT ANGLE.

**Question no – (6) **

**Solution : **

**Figure – (a)**

= x° + 40° = 180

= x° = 180° – 40°

= 140°

**Figure – (b)**

= x° = 180° – 60°

= 120°

**Figure – (c)**

= x° = 180° – 70°

= 110°

**Figure – (d)**

= x° = 180° – 110°

= 70°

**Question no – (7) **

**Solution : **

**Figure – (a)**

= 90° – 20°

= 70°

**Figure – (b)**

= b° = 90° – 41°

= 49°

**Question no – (8) **

**Solution : **

No, the measure of an angle does not change if we view it through a magnifying glass.

**Question no – (9) **

**Solution : **

**Figure – (a) **

Angle |
Type of angle |

∠ABC | Right |

∠BAD | Obtuse |

∠AED | Right |

∠AEC | Straight |

∠BED | Straight |

∠ADE | Acute |

**Figure – (b) **

Angle | Type of angle |

∠BCD | Obtuse |

∠QPT | Acute |

∠PTS | Obtuse |

∠TSR | Right |

∠QRS | Right |

∠PQR | Obtuse |

**Try These 12 (i) : **

**Question no – (1) **

**Solution : **

The correct option is – (d) CD = 7 cm, this is False.

**Question no – (2) **

**Solution : **

The angle measure 90° of the two set squares kept in your geometry box is common.

**Question no – (3) **

**Solution : **

The incorrect option is – (d) m ⊥ BH

**Understanding Elementary Shapes Exercise 12.5 Solution**

**Question no – (1) **

**Solution : **

Figure – **(a)** Isosceles, acute – angled.

Figure – **(b)** Equilateral, acute angled.

Figure – **(c)** Scalene, right – angular.

Figure – **(d)** Scalene, obtuse angular.

Figure – **(e)** Scalene, obtuse- angular.

Figure – **(d)** Scalene, obtuse angular.

**Question no – (2) **

**Solution : **

**(a)** In AABC, AB = 7.5 cm, BC = 8 cm, CA = 10 cm.

= Scalene

**(b)** In ADEF, DE = EF = DF = 6 cm.

= Equilateral

**(c)** In AGHI, GH = 15 cm, HI = 15 cm, GI = 18 cm.

= Isosceles

**Question no – (3) **

**Solution : **

**(a)** In AABC, ∠A = 30°, B = 70°, 2C=80°.

= Acute- angled

**(b)** In APQR, ∠P 90°, ∠Q = 45°, ∠R = 45°.

= Right – angled

**(c)** In ALMN, ∠L = 95°, ∠M = 50°, ∠N = 35°.

= Obtuse – angled

**Question no – (4) **

**Solution : **

**(a)** The measure of each angle of an equilateral triangle is Equal.

**(b)** The other name for a regular triangle is Equilateral Triangle.

**(c)** A triangle having two sides equal is called an Isosceles Triangle.

**(d)** A triangle having all sides different will have all angles Scalene.

**Question no – (5) **

**Solution : **

Measures of Triangle |
Type of triangle |

(i) 3 sides of equal length | (e) Equilateral |

(ii) 2 sides of equal length | (g) Isosceles |

(iii) ll sides are of different | (a) Scalene |

(iv) 3 acute angles | (f) Acute – angled |

(v) 1 right angle | (d) Right angled |

(vi) 1 obtuse angle | (c) Obtuse angled |

(vii) 1 right angle with two sides of equal length | (b) Isosceles right angled |

**Try These 12 (ii) **

**Question no – (1) **

**Solution : **

Correct option is – **(b)** acute – angled.

Triangle whose all angles are less than 90° is of type acute – angled

**Question no – (2) **

**Solution : **

Correct option is – **(d)** none

In a scalene triangle, none angles are equal.

**Question no – (3) **

**Solution : **

Correct option is – **(c)** equilateral.

If each side of a triangle is 5.6 cm, then it will be equilateral triangle.

**Understanding Elementary Shapes Exercise 12.6 Solution**

**Question no – (1) **

**Solution : **

**(a) Difference between the Trapezium and Parallel are as follows :**

**Trapezium :**

**(i)** One pair of sides are not parallel (Opposite)

**(ii)** No necessarily

**(iii)** Sum of two adjacent angles is 180°

**Parallel :**

**(i)** Each pair of sides are parallel (Opposite)

**(ii)** Opposite sides are equal to each other

**(iii)** Sum of two opposite is 180°

**(b) Difference between the Square and Rhombus are as follows :**

**Square :**

**(i)** Adjacent angle are equal.

**(ii)** Two diagonals are equal.

**Rhombus :**

**(i)** Adjacent angles are not equal

**(ii)** Diagonals are not equal

**Question no – (2) **

**Solution : **

We can describe the regular quadrilateral in __Square.__

**Question no – (3) **

**Solution : **

**(a)** Every square is a rectangle.

= This statement is **True**

**(b)** Every parallelogram is a trapezium

= This statement is **False**

**(c)** Every rhombus is a square

= This statement is **False**

**(d)** Every rectangle is a square

= This statement is **False**

**(e)** Every parallelogram

= This statement is **False**

**(f)** Every rectangle is a parallelogram

= This statement is **True**

**(g)** All the sides of a parallelogram are equal length.

= This statement is **False**

**(h)** Each angle of square is a right angle

= This statement is **True.**

**Question no – (4) **

**Solution : **

**(a) Two properties of the Square are –**

**(i)** All sides of a square are equal.

**(ii)** All angles of a square are equal.

**(b) Two properties of the Rectangle are –**

**(i)** Each interior angle of a rectangle is equal to 90 degrees.

**(ii)** Both the diagonals of a rectangle have the same length.

**(c) Two properties of a Parallelogram are –**

**(i)** The opposite sides of a parallelogram are parallel and congruent.

**(ii)** The two diagonals of a parallelogram bisect each other.

**(d) Two properties of a rhombus are –**

**(i)** All sides of the rhombus are equal.

**(ii)** The opposite sides of a rhombus are parallel.

**Try These 12 (iii) **

**Question no – (1) **

**Solution : **

Figure – **(a)** is not a polygon

Figure – **(b)** is a polygon.

Figure – **(c)** is not a polygon

Figure – **(d)** is not a polygon.

**Question no – (2) **

**Solution : **

Correct answer is option – **(b)**

The minimum number of sides a polygon can have 3 sides.

**Question no – (3) **

**Solution : **

Figure – **(a)** is a Quadrilateral.

Figure – **(b)** is a Triangle.

Figure – **(c)** is a Pentagon.

Figure – **(d)** is a Hexagon.

Figure – **(e)** is a Octagon.

**Question no – (4) **

**Solution : **

**No,** rhombus is not a regular polygon.

Because, it’s all angles are not equal.

**Understanding Elementary Shapes Exercise 12.7 Solution**

**Question no – (1) **

**Solution : **

The name of figure **(a)** is cuboid.

The name of figure **(b)** is square pyramid.

The name of figure **(c)** is cylinder.

**Question no – (3) **

**Solution : **

**(a)** The shape of a geometry box is **Cuboid.**

**(b)** The shape of a ball is **Sphere.**

**(c)** The shape of a die is **Cube.**

**(d)** The shape of a brick is **Cuboid.**

**(e)** The shape of a road-roller is **Cylinder**

**(f)** The shape of a ice-cream cone is **Cone.**

**Question no – (4) **

**Solution : **

The shape of the faces of a cube is **Square.**

The shape of the faces of a cuboid is **Rectangle.**

**Question no – (5) **

**Solution : **

(a) **Cuboid** has six plane faces.

(b) **Cone** has 1 curved surface and 1 plane surface.

(c) **Cylinder** shape has 2 plane faces and 1 curved face.

(d) **Sphere** shape has no plane surface but have only one curved surface.

(e) **Prism** shape has 3 rectangular faces and 2 triangular faces of equal size.

(f) **Cube** shape has all the faces a square.

(e) **Pyramid** shape has 4 faces looking like triangular regions.

**Question no – (7) **

**Solution : **

In the given figure, there are total 14 cubes are present.

**Question no – (8) **

**Solution : **

5 more smaller cubes are required to complete the given cube.

**Understanding Elementary Shapes Chapter Check-up Solution : **

**Question no – (2) **

**Solution : **

**(a) 5 to 8**

= 3/12

= 1/4

Thus, 1/4 fraction of a clockwise revolution will minute hand turn.

**(b) 6 to 10**

= 4/12

= 1/3

Thus, 1/3 fraction of a clockwise revolution will minute hand turn.

**Question no – (3) **

**Solution : **

**(a)** If hand of a clock starts at 4 and make of 3/4 revolution clockwise, then it will stops at 1.

**(b)** If hand of a clock starts at 5 and take 1/4 of revolution anti-clockwise, then it will stops at 2.

**Question no – (4) **

**Solution : **

**In the Figure – (A)**

**(I)** ∠PQS

= Acute

**(II)** ∠PSR

= Obtuse

**(III)** ∠QRS

= Acute

**(IV)** ∠PRQ

= Acute

**In the Figure – (B)**

**(I)** ∠VXY

= Obtuse

**(II)** ∠XYZ

= Obtuse

**(III)** ∠XZY

= Acute

**(IV)** ∠VOZ

= Obtuse

**Question no – (5) **

**Solution : **

The net of a cuboid,

**Question no – (6) **

**Solution : **

**(a)** If you start facing South and turn clockwise to west, then you will turn 1/4 part of revolution.

**(b)** If you start facing North and turn anticlockwise to east, then you will turn 3/4 part of revolution.

**(c)** If you start facing East and turn clockwise to north, then you will turn 3/4 part of revolution.

**(d)** If you start facing North and turn anticlockwise to west, then you will turn 1/4 part of revolution.

**Question no – (7) **

**Solution : **

**(a)** Yes, a triangle can have two acute angles.

**(b)** No, a triangle cannot have two obtuse angles.

**(c)** No, a triangle cannot have two right angle.

**(d)** No, a triangle cannot have one obtuse and one right angle.

**Question no – (8) **

**Solution : **

**(a) a scalene acute-angled triangle,**

**(b) a right-angled isosceles triangle,**

**(c) a scalene right-angled triangle,**

**Question no – (9) **

**Solution : **

**(a)** a rectangle

= ABCF

**(b)** a parallelogram

= ABDE

**(c)** a trapezium

= ABGE

**(d)** a right-angled triangle

= BCG/ AFE/ BCD

**Question no – (11) **

**Solution : **

**(a) Cube**

= dice, Rubik’s cube

**(b) Cuboid**

= Match box, Brick

**(c) Cylinder**

= LPG cylinder, Water tank

**(d) Cone**

= Ice-cream cone

**(e) Sphere**

= Football, tennis ball

**Question no – (12) **

**Solution : **

**(a)** Edges = AB, BC, CD, DA, EF, FG, GH, HE, AE, BF, CG, DH

**(b)** Faces = ABCD, EFGH, ADHG, AEFB, BCGF, CDHG

**(c)** Top = ABCD

**(d)** Bottom = EFGH

**Question no – (13) **

**Solution : **

**(a)** briefcase → (iii) cuboid

**(b)** Gas cylinder → (iv) cylinder

**(c)** Road roller → (iv) cylinder

**(d)** Globe → (i) sphere

**(e)** Ice-cream brick → (iii) cuboid

**(f)** Sugar cube → (ii) cube

**(g)** Water bottle → (iv) cylinder

**(h)** Book → (iii) cuboid

**(i)** Dice → (ii) cube

**(j)** Birthday cap → (v) cone

**(k)** Ice-cream cone → (v) cone

**Question no – (14) **

**Solution : **

All squares are a rectangle but all rectangles are not square.

Reason : In squares the adjacent sides are equal to each other. But in rectangle, it’s not.

**Question no – (15) **

**Solution : **

I | R | T | |||||||||||

I | S | O | S | C | E | L | E | S | R | ||||

F | I | ||||||||||||

L | A | ||||||||||||

E | N | ||||||||||||

X | G | ||||||||||||

L | |||||||||||||

R | H | O | M | B | U | S | Q | U | A | R | E |

**Question no – (16) **

**Solution :**

**Parallelogram :**

**Rhombus :**

**Square :**

**Rectangle :**

**Previous Chapter Solution : **