Maharashtra Board Class 6 Maths Chapter 16 Quadrilaterals Set 37 Solutions

Question 1. Observe the figures below and find out their names:
ℹ️ चित्र व्याख्या (Diagram Explanation): पहले चित्र में पाँच भुजाओं वाला एक बंद बहुभुज है। दूसरे चित्र में छह भुजाओं वाला एक बंद बहुभुज है। तीसरे चित्र में सात भुजाओं वाला एक बंद बहुभुज है। चौथे चित्र में आठ भुजाओं वाला एक बंद बहुभुज है।
Answer:
(i) Pentagon (5 sides)
(ii) Hexagon (6 sides)
(iii) Heptagon (7 sides)
(iv) Octagon (8 sides)
In simple words: The number of sides determines the name of the polygon: 5 sides for a pentagon, 6 for a hexagon, 7 for a heptagon, and 8 for an octagon.

🎯 Exam Tip: Remember the prefixes for different numbers of sides (penta-, hexa-, hepta-, octa-) to correctly name polygons. This is a basic recall question.

Maharashtra Board Class 6 Maths Chapter 16 Quadrilaterals Practice Set 37 Intext Questions and Activities

Question 1. Observe the figures given below and say which of them are quadrilaterals.
ℹ️ चित्र व्याख्या (Diagram Explanation): पहले चित्र में चार भुजाओं वाला एक बंद बहुभुज है, जिसके शीर्ष A, B, C, D हैं। दूसरा चित्र एक तीर के आकार का बहुभुज है। तीसरा चित्र एक क्रॉस या X-आकार का बहुभुज है। चौथा चित्र एक घर के आकार का बहुभुज है।
Answer: Is a quadrilateral: (i)
In simple words: A quadrilateral is a closed two-dimensional shape with exactly four straight sides and four angles. Only figure (i) fits this definition.

🎯 Exam Tip: Focus on the definition of a quadrilateral-a closed figure with exactly four straight sides-to identify it correctly. Count the sides and check if the figure is closed.

Question 2. Draw a quadrilateral. Draw one diagonal of this quadrilateral and divided it into two triangles. Measures all the angles in the figure. Is the sum of the measures of the four angles of the quadrilateral equal to the sum of the measures of the six angles of the two triangles? Verity that this is so with other quadrilaterals.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक चतुर्भुज PQRS को दर्शाता है, जिसमें एक विकर्ण PR खींचा गया है। यह विकर्ण चतुर्भुज को दो त्रिभुजों, PQR और PRS में विभाजित करता है। विभिन्न कोणों के माप दिए गए हैं।
Answer:
m∠PQR = 104°
m∠QRP = 26°
m∠RPQ = 50°
m∠PRS = 34°
m∠RSP = 106°
m∠SPR = 40°
Therefore, Sum of the measures of the angles of quadrilateral = m∠PQR + m∠QRP + m∠RPQ + m∠PRS + m∠RSP + m∠SPR
= 104° + 26° + 50° + 34° + 106° + 40°
= 360°
Also, we observe that
Sum of the measures of the angles of quadrilateral = Sum of the measures of angles of the two triangles (PQR and PRS)
= (104°+ 26°+ 50°)+ (34° + 106° + 40°)
= 180° + 180°
= 360°
[Note: Students should drew different quadrilaterals and verify the property.]
In simple words: When a diagonal divides a quadrilateral into two triangles, the sum of the angles of the quadrilateral is equal to the sum of the angles of these two triangles, which is 360 degrees. Each triangle's angles sum to 180 degrees.

🎯 Exam Tip: Understanding that a quadrilateral can be divided into two triangles is key to proving that the sum of its interior angles is 360°. This property is fundamental for solving problems related to quadrilaterals.

Question 3. For the pentagon shown in the figure below, answer the following:
ℹ️ चित्र व्याख्या (Diagram Explanation): पहले चित्र में एक तारा-आकार का बहुभुज है। दूसरे चित्र में A, B, C, D, E शीर्षों वाला एक पंचकोण (pentagon) दिखाया गया है। तीसरे चित्र में कुछ बच्चे एक गोला बनाकर खड़े हैं, जो पंचकोण का आकार बना रहे हैं।
Answer:
1. The vertices of the pentagon are points A, B, C, D and E.
2. The sides of the pentagon are segments AB, BC, CD, DE and EA.
3. The angles of the pentagon are ∠ABC, ∠BCD, ∠CDE, ∠DEA and ∠EAB.
4. The players shown in the above figure form a pentagon. The players are standing on the vertices of
In simple words: A pentagon is a polygon with five vertices, five sides, and five interior angles. The players demonstrate how these vertices can be points in space.

🎯 Exam Tip: Identify the vertices, sides, and angles of a polygon by systematically listing them. Vertices are points, sides are line segments connecting vertices, and angles are formed at the vertices.

Question 4. Cut out a paper in the shape of a quadrilateral. Make folds in it that join the vertices of opposite angles. What can these folds be called?
ℹ️ चित्र व्याख्या (Diagram Explanation): पहले चित्र में एक चतुर्भुज की आकृति है। दूसरे चित्र में एक चतुर्भुज को विपरीत शीर्षों को जोड़ते हुए मोड़ा गया है, जिससे विकर्ण बन रहे हैं। तीसरे चित्र में भी एक मुड़ा हुआ चतुर्भुज दिखाया गया है।
Answer: The folds are called diagonals of the quadrilateral.
In simple words: When you fold a quadrilateral to connect opposite corners, the crease lines formed are called diagonals.

🎯 Exam Tip: A diagonal in a polygon connects two non-adjacent vertices. Understanding this practical demonstration helps visualize diagonals in various quadrilaterals.

Question 5. Take two triangular pieces of paper such that. one side of one triangle is equal to one side of the other. Let us suppose that in ΔΑΒC and ΔPQR, sides AC and PQ are the equal sides. Join the triangles so that their equal sides lie B side by side. What figure do we get?
ℹ️ चित्र व्याख्या (Diagram Explanation): पहले चित्र में एक त्रिभुज ABC दिखाया गया है। दूसरे चित्र में एक त्रिभुज PQR दिखाया गया है। तीसरा चित्र यह दर्शाता है कि जब दो त्रिभुजों को उनकी बराबर भुजाओं (AC और PQ) के साथ जोड़ा जाता है, तो एक नया चतुर्भुज बनता है।
Answer: If we place the triangles together such that the equal sides overlap, the two triangles form a quadrilateral.
In simple words: By joining two triangles along an equal side, you create a new shape which is a quadrilateral.

🎯 Exam Tip: This activity demonstrates how complex shapes can be composed of simpler ones. It reinforces the idea that a quadrilateral can be seen as two triangles joined along a common side.