Understanding Quadrilaterals Worksheet

Fill in the blanks Type Questions

1. Different sign boards might have been seen at the signal or close to the roadways. While going through the streets and roads, Roshan came across several types of boards. The boards come in a variety of shapes, as demonstrated below:
   
   The number of boards that are not polygons is _____________.
   
   
2. When it rains, cracked roadways are a typical occurrence. One of them is displayed:
   
   Several polygonal shapes are created by the fissures (assuming they are thought of as straight). Consider the highlighted polygon whose measures of the angles are as follows:
   
   Then the value of x is ____________.
   
   
3. A cupboard placed in Kabir’s room is rectangular in shape. As the cupboard is little old so Kabir plans to paste stickers on it and for that he needs to know the width and height of the cupboard. If the dimensions are follows:
   
   Then, the values of x and y are __________ and ___________ respectively.
   
   
4. For the Diwali Pooja, Anju's mother is preparing sweet "kaju katli". She is using a cutter to make the treat, as shown below:
   
   Each kaju katli is precisely sliced with a cutter, resulting in a rhombus. If each kaju katli's measurements are as follows:
   
   Then the value of z is ___________.
   
   Multiple Choice Questions
   
   
5. It’s a math fest at Poonam’s school and so she thought of wearing a t-shirt with some math on it. She wore the t-shirt which is shown below:
   
   It contains three geometric figures, each of which has eyes and legs. What is the number of polygons present on the t-shirt? 
   (a)0
   (b)1
   (c)2
   (d)3
   
   
6. A commercial building has been made in a weird structure with few polygonal shapes in it as given below:
   
   The polygonal shapes are highlighted with a wide boundary. How many concave polygons can be found in the structure of this building? 
   (a)0
   (b)2
   (c)4
   (d)5
   
   
7. As the Independence Day is near, every shop has different shapes of stickers with flag of India printed on it. Sticker’s available at Mohan’s shop are as given below:
   
   How many stickers are in the shape of convex polygon?
   (a)2
   (b)3
   (c)4
   (d)5
   
   
8. You may have observed that every church has a cross sign, which is a representation of Christianity.
   
   While the cross symbol on the church is a representation of Christianity, closer inspection reveals that it actually has a polygonal shape. What is the sum of the measures of the external angles of this polygon?
   (a)90°
   (b)180°
   (c)270°
   (d)360°
   
   
9. A bridge over a railway track has been made for the convenience of people so that they can move from one side to another easily.
   
   Which type of quadrilateral is formed by the shape of the bridge given in the picture? 
   (a)Trapezium
   (b)Kite
   (c)Parallelogram
   (d)Rhombus
   
   
10. A mirror in John’s room broke down into several pieces and so he threw it away. He now needed a new mirror for his room and that’s the reason he looked at the pictures shown below:
    
    How many of the kite-shaped mirrors in the photographs are there?
    (a)2
    (b)3
    (c)7
    (d)9
    
    
11. A building is made in such a way that the opposite sides are parallel to each other.
    
    Which type of a quadrilateral is seen in this picture?
    (a)Kite
    (b)Parallelogram
    (c)Square
    (d)Rectangle
    
    
12. Look at the roof of this house which is situated far from the city.
    
    The owner wants to install a new roof as the old one has a leakage. If the measurements are as given in the figure below, find the unknown length ‘x’ so that he can install the rooftop properly.
    (a)16 feet
    (b)15 feet
    (c)8 feet
    (d)30 feet
    
    
13. Since everyone has switched over to smart TVs from traditional models. In response to Ravi's request, his father also intends to install a smart TV. Although the new TV is larger than the old one, its length must be less than 50 inches to fit in the hallway. If the measurements are as stated below:
    
    Find the appropriate length to assist Ravi in purchasing a TV.
    (a)28 inches
    (b)36 inches
    (c)48 inches
    (d)60 inches
    
    Subjective Questions
    
    
14. Most of us follow a trend of making sweets and snacks for festivals. This time, Gopal has decided to bake some cookies and went to the nearby store to hunt for various cookie cutters. The shopkeeper displayed the following cookie cutters:
    
    How many cookie cutters did Gopal buy if he only purchased those that would provide polygonal-shaped cookies?
    
    
15. As the new academic year started, Vinny has been promoted to the next class. Before school resumes, she wants to buy a cartoon shaped rubber. The rubbers shown at the shop are given below:
    
    If only borders are considered, check whether the number of regular polygons is same as the number of irregular polygons or not.
    
    
16. There are different variety of fishes available in a sea. One of them looks like a polygon which is a start fish as shown below.
    
    If the boundary is considered, explain whether it makes a regular polygon or an irregular polygon?
    
    
17. Juhi bought a new plot which is near to her old house. She gave the contract to Sachin but want tiles of her choice. So, she went to the shop and selected a tile which is in the shape of a polygon. If the angles made in this polygon are as given in the figure below, find the values of unknown angles.
    
    
    
18. Madhuri plans to make a cat house using a cardboard and some empty paper rolls. She just build the structure and is looking for some more things to complete the house. The structure she made is shown below along with the measurements:
    
    If AC = z, which is 6 cm less than BD, then find the values of the unknown x, y, z.
    
    
19. Raunak is planning to order earring for her daughter. However, he will only place an order if the earrings' length is less than 9 cm. Now that the measurements have been given, Raunak orders the earrings in accordance with them. If the data (consider in cm) are as shown below:
    
    Did Raunak correctly compute the length?
    
    
20. There are three equal sections in a window each section in the shape of a square. If the dimensions are as follows:
    
    Find the height of the window (Excluding the top and bottom wooden parts).

Fill in the blanks Type Questions

1. Different sign boards might have been seen at the signal or close to the roadways. While going through the streets and roads, Roshan came across several types of boards. The boards come in a variety of shapes, as demonstrated below:
   
   The number of boards that are not polygons is _____________.
   
   Correct Answer: 2
   Solution:
   A simple closed curve made up of only line segments is called a polygon.
   So, the images 3rd and 4th are not polygons.
   Thus, the number of boards that are not polygons is 2.
   
   
2. When it rains, cracked roadways are a typical occurrence. One of them is displayed:
   
   Several polygonal shapes are created by the fissures (assuming they are thought of as straight). Consider the highlighted polygon whose measures of the angles are as follows:
   
   Then the value of x is ____________.
   
   Correct Answer: 50
   Solution:
   We know that the sum of exterior angles of a polygon is 360°.
   ⇒ (x – 2)° + (x – 5)° + (x + 12)° + 2x° + (2x + 5)° = 360°
   ⇒ (x – 2) + (x – 5) + (x + 12) + 2x + (2x + 5) = 360
   ⇒ 7x + 10 = 360
   ⇒ 7x = 350
   ⇒ x = 50
   So, the value of x is 50.
   
   
3. A cupboard placed in Kabir’s room is rectangular in shape. As the cupboard is little old so Kabir plans to paste stickers on it and for that he needs to know the width and height of the cupboard. If the dimensions are follows:
   
   Then, the values of x and y are __________ and ___________ respectively.
   
   Correct Answer: 2, 1
   Solution:
   Opposite sides of a rectangle are equal.
   ⇒ 2x + 2 = 4x – 2 
   ⇒ 4x – 2x = 2 + 2
   ⇒ 2x = 4
   ⇒ x = 2
   Also, y + 2 = 3y
   ⇒ 3y – y = 2
   ⇒ 2y = 2
   ⇒ y = 1
   So, the values of x and y are 2 and 1 respectively.
   
   
4. For the Diwali Pooja, Anju's mother is preparing sweet "kaju katli". She is using a cutter to make the treat, as shown below:
   
   Each kaju katli is precisely sliced with a cutter, resulting in a rhombus. If each kaju katli's measurements are as follows:
   
   Then the value of z is ___________.
   
   Correct Answer: 5
   Solution:
   All sides of a rhombus are equal.
   ⇒ 3z – 2 = 2z + 3
   ⇒ 3z – 2z = 3 + 2
   ⇒ z = 5
   So, the value of z is 5.
   
   Multiple Choice Questions
   
   
5. It’s a math fest at Poonam’s school and so she thought of wearing a t-shirt with some math on it. She wore the t-shirt which is shown below:
   
   It contains three geometric figures, each of which has eyes and legs. What is the number of polygons present on the t-shirt? 
   (a)0
   (b)1
   (c)2
   (d)3
   
   Correct Option: (b) 1
   Solution:
   The figures formed are:
   
   Out of these only the 3rd figure is a polygon.
   Hence, the number of polygons present on the t-shirt is 1.
   
   
6. A commercial building has been made in a weird structure with few polygonal shapes in it as given below:
   
   The polygonal shapes are highlighted with a wide boundary. How many concave polygons can be found in the structure of this building? 
   (a)0
   (b)2
   (c)4
   (d)5
   
   Correct Option: (b) 2
   Solution:
   Polygonal shapes present in the structure are:
   
   Concave polygons have at least one diagonal whose portion is in the exterior of the polygon.
   Polygon 3 and polygon 6 are concave polygons.
   Hence, 2 concave polygons can be found in the structure of the building.
   
   
7. As the Independence Day is near, every shop has different shapes of stickers with flag of India printed on it. Sticker’s available at Mohan’s shop are as given below:
   
   How many stickers are in the shape of convex polygon?
   (a)2
   (b)3
   (c)4
   (d)5
   
   Correct Option: (a) 2
   Solution:
   Convex polygons have no portions of their diagonals in the exterior of the polygon.
   Stickers shown in the following images are in the shape of a polygon:
   
   In these, polygon made in the 1st flag (in the above image) is concave.
   Hence, there are only 2 stickers that are in the shape of a convex polygon.
   
   
8. You may have observed that every church has a cross sign, which is a representation of Christianity.
   
   While the cross symbol on the church is a representation of Christianity, closer inspection reveals that it actually has a polygonal shape. What is the sum of the measures of the external angles of this polygon?
   (a)90°
   (b)180°
   (c)270°
   (d)360°
   
   Correct Option: (d) 360°
   Solution:
   The cross symbol on the Church is in the shape of a polygon.
   We know that, the sum of all the exterior angles of a polygon is 360°.
   Hence, the sum of the measures of the external angles of this polygon is 360°.
   
   
9. A bridge over a railway track has been made for the convenience of people so that they can move from one side to another easily.
   
   Which type of quadrilateral is formed by the shape of the bridge given in the picture? 
   (a)Trapezium
   (b)Kite
   (c)Parallelogram
   (d)Rhombus
   
   Correct Option: (a) Trapezium
   Solution:
   When we carefully observe the shape of the bridge, it is found to be a trapezium as it has four sides and only one pair of opposite sides are parallel.
   Hence, the quadrilateral formed by the shape of the bridge given in the picture is a trapezium.
   
   
10. A mirror in John’s room broke down into several pieces and so he threw it away. He now needed a new mirror for his room and that’s the reason he looked at the pictures shown below:
    
    How many of the kite-shaped mirrors in the photographs are there?
    (a)2
    (b)3
    (c)7
    (d)9
    
    Correct Option: (b) 3
    Solution:
    If we look closely at the Image 4, it has three mirrors and all are in the shape of a kite.
    
    Hence, there are 3 kite-shaped mirrors present in the photographs.
    
    
11. A building is made in such a way that the opposite sides are parallel to each other.
    
    Which type of a quadrilateral is seen in this picture?
    (a)Kite
    (b)Parallelogram
    (c)Square
    (d)Rectangle
    
    Correct Option: (b) Parallelogram
    Solution:
    When we closely observe the picture, the quadrilateral formed has its opposite sides parallel.
    
    Hence, it is a parallelogram.
    
    
12. Look at the roof of this house which is situated far from the city.
    
    The owner wants to install a new roof as the old one has a leakage. If the measurements are as given in the figure below, find the unknown length ‘x’ so that he can install the rooftop properly.
    (a)16 feet
    (b)15 feet
    (c)8 feet
    (d)30 feet
    
    Correct Option: (c) 8 feet
    Solution:
    When we closely observe the picture, the quadrilateral formed has its opposite sides parallel.
    In a parallelogram, the pair of opposite sides are of equal length.
    ⇒ x = 8 feet
    
    
13. Since everyone has switched over to smart TVs from traditional models. In response to Ravi's request, his father also intends to install a smart TV. Although the new TV is larger than the old one, its length must be less than 50 inches to fit in the hallway. If the measurements are as stated below:
    
    Find the appropriate length to assist Ravi in purchasing a TV.
    (a)28 inches
    (b)36 inches
    (c)48 inches
    (d)60 inches
    
    Correct Option: (c) 48 inches
    Solution:
    Given: Height of the TV = 28 inches
    We know that, a TV is always in a rectangle shape and this can concluded from the image as well.
    So, its opposite sides are equal.
    ⇒ 9m + 3 = 10m – 2
    ⇒ 10m – 9m = 3 + 2
    ⇒ m = 5
    ⇒ 9m + 3 = 9×5 + 3 = 48 
    Thus, the length of the TV is 48 inches.
    
    Subjective Questions
    
    
14. Most of us follow a trend of making sweets and snacks for festivals. This time, Gopal has decided to bake some cookies and went to the nearby store to hunt for various cookie cutters. The shopkeeper displayed the following cookie cutters:
    
    How many cookie cutters did Gopal buy if he only purchased those that would provide polygonal-shaped cookies?
    
    Solution:
    The cookie cutters that would provide polygonal shape are given below:
    
    There are 6 such cutters.
    Hence, Gopal will buy 6 cookie cutters.
    
    
15. As the new academic year started, Vinny has been promoted to the next class. Before school resumes, she wants to buy a cartoon shaped rubber. The rubbers shown at the shop are given below:
    
    If only borders are considered, check whether the number of regular polygons is same as the number of irregular polygons or not.
    
    Solution:
    The polygons formed by the rubbers are given below:
    
    Regular polygons have their sides equal.
    The last three polygons (star shaped) are regular whereas the other three are irregular polygons.
    Hence, the number of regular polygons is same as the number of irregular polygons. 
    
    
16. There are different variety of fishes available in a sea. One of them looks like a polygon which is a start fish as shown below.
    
    If the boundary is considered, explain whether it makes a regular polygon or an irregular polygon?
    
    Solution:
    When the boundary are considered, we get the following polygon:
    
    All the sides of this polygon looks equal and hence it is a regular polygon.
    
    
17. Juhi bought a new plot which is near to her old house. She gave the contract to Sachin but want tiles of her choice. So, she went to the shop and selected a tile which is in the shape of a polygon. If the angles made in this polygon are as given in the figure below, find the values of unknown angles.
    
    
    Solution:
    We know that the sum of all exterior angles of a polygon is 360°.
    ⇒ (2m – 10)° + 90° + (2m + 10)° + (m + 4)° + (m + 16)° + (m + 5)° = 360°
    ⇒ (2m – 10) + 90 + (2m + 10) + (m + 4) + (m + 16) + (m + 5) = 360
    ⇒ 7m + 115 = 360
    ⇒ 7m = 245
    ⇒ m = 35
    So, we have
    (2m – 10)° = (2×35 – 10) ° = 60°
    (2m + 10)° = (2×35 + 10)° = 80
    (m + 4)° = (35 + 4)° = 39°
    (m + 16)° = (35 + 16)° = 51°
    (m + 5)° = (35 + 5)° = 40°
    Thus, the unknown angles are 60°, 80°, 39°, 51° and 40°.
    
    
18. Madhuri plans to make a cat house using a cardboard and some empty paper rolls. She just build the structure and is looking for some more things to complete the house. The structure she made is shown below along with the measurements:
    
    If AC = z, which is 6 cm less than BD, then find the values of the unknown x, y, z.
    
    Solution:
    Opposite angles of a parallelogram are equal in measure.
    ⇒ x° = 115°
    ⇒ x = 115
    Also, adjacent angles in a parallelogram are supplementary.
    ⇒ ∠ABO + 40° + 115° = 180°
    ⇒ ∠ABO = 25°
    Now, y° = ∠ABO
    ⇒ y° = 25°
    ⇒ y = 25
    Here, BO = OD … Diagonals bisect each other
    ⇒ OD = 15 cm
    ⇒ BD = BO + OD = 30 cm
    It is given that, AC is 6 less than BD.
    ⇒ AC = BD – 6 cm = 30 – 6 = 24 cm.
    Hence, x = 115, y = 25 and z = 24 cm.
    
    
19. Raunak is planning to order earring for her daughter. However, he will only place an order if the earrings' length is less than 9 cm. Now that the measurements have been given, Raunak orders the earrings in accordance with them. If the data (consider in cm) are as shown below:
    
    Did Raunak correctly compute the length?
    
    Solution:
    A quadrilateral given in the figure has lengths of all its sides equal but the angles are not right angles.
    So, it is a rhombus.
    Since, the diagonals of a rhombus are perpendicular bisectors of one another.
    ⇒ 9x – 5 = 5x – 1
    ⇒ 9x – 5x = 5 – 1
    ⇒ 4x = 4
    ⇒ x = 1
    ⇒ 9x – 5 = 4 and 5x – 1 = 4
    Height of the rhombus = (9x – 5) + (5x – 1) = 8 cm
    So, the length of the earring is 8 cm which is less than 9 cm.
    Hence, Raunak compute the length correctly.
    
    
20. There are three equal sections in a window each section in the shape of a square. If the dimensions are as follows:
    
    Find the height of the window (Excluding the top and bottom wooden parts).
    
    Solution:
    All the sides of a square are equal.
    So, height of each section is 15 cm.
    Now, as every section of a window is in the shape of a square and all the three sections of a window are equal.
    ⇒ Height of the window = 3 × Height of one section = 3 × 15 cm = 45 cm