Maharashtra Board Class 6 Maths Chapter 16 Quadrilaterals Set 38 Solutions

Question 1. Draw XYZW and answer the following:
(i) The pairs of opposite angles.
(ii) The pairs of opposite sides.
(iii) The pairs of adjacent sides.
(iv) The pairs of adjacent angles.
(v) The diagonals of the quadrilateral.
(vi) The name of the quadrilateral in different ways.
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक चतुर्भुज XYZW दर्शाया गया है जिसके शीर्षों को वामावर्त दिशा में नामांकित किया गया है। X, Y, Z और W शीर्ष हैं। चतुर्भुज के अंदर दो विकर्ण XZ और YW खींचे गए हैं, जो चतुर्भुज को दो त्रिभुजों में विभाजित करते हैं।
i. a. ∠XYZ and ∠XWZ
b. ∠YXW and ∠YZW
ii. a. side XY and side WZ
b. side XW and side YZ
iii. a. side XY and side XW
b. side WX and side WZ
c. side ZW and side ZY
d. side YZ and side YX
iv. a. ∠XYZ and ∠YZW
b. ∠YZW and ∠ZWX
c. ∠ZWX and ∠WXY
d. ∠WXY and ∠XYZ
v. Seg XZ and seg YW
vi. Rs.XYZW
Rs.YZWX
Rs.ZWXY
Rs.WXYZ
Rs.XWZY
Rs.WZYX
Rs.ZYXW
Rs.YXWZ
In simple words: This question asks for the different properties and naming conventions of a quadrilateral XYZW, including its opposite/adjacent angles and sides, and its diagonals. The answers list these elements based on the drawn figure.

🎯 Exam Tip: Accurately identifying opposite and adjacent parts of a quadrilateral is crucial for scoring. Practice naming quadrilaterals in all possible orders.

Question 2. In the table below, write the number of sides the polygon has.
Answer:

In simple words: This question requires recalling the number of sides associated with various common polygons, such as a quadrilateral having 4 sides and a hexagon having 6 sides.

🎯 Exam Tip: Memorizing the prefixes for polygon names (e.g., "quad-" for four, "penta-" for five, "hexa-" for six) is essential for quickly determining the number of sides.

Question 3. Look for examples of polygons in your surroundings. Draw them.
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक सेट स्क्वायर का चित्र है जो एक त्रिभुज को दर्शाता है। एक भारतीय ध्वज का चित्र है जो आयताकार आकृति को दर्शाता है। भिंडी (लेडी फिंगर) के अनुप्रस्थ काट का चित्र है जो पंचकोणीय आकृति को दर्शाता है। शहद के छत्ते के एक चैंबर का चित्र है जो षट्कोणीय आकृति को दर्शाता है।
Set square (Triangle)
Flag (Rectangle)
Cross section of Lady finger (Pentagon)
Honey comb chamber (Hexagon)
In simple words: This question asks students to identify common objects in their environment that represent various polygons, like a triangular set square, a rectangular flag, a pentagonal ladyfinger slice, and a hexagonal honeycomb.

🎯 Exam Tip: Being able to connect geometric shapes to real-world objects demonstrates strong conceptual understanding. Focus on examples that clearly show the polygon's sides and angles.

Question 4. We see polygons when we join the tips of the petals of various flowers. Draw these polygons and write down the number of sides of each polygon.
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): सफेद ट्रिलियम फूल का चित्र है, जिसके तीन पंखुड़ियों के सिरे जुड़कर एक त्रिभुज बनाते हैं। सदाबहार (पेरिविंकल) फूल का चित्र है, जिसकी पांच पंखुड़ियों के सिरे जुड़कर एक पंचकोण बनाते हैं। मॉर्निंग मीडो फूल का चित्र है, जिसकी चार पंखुड़ियों के सिरे जुड़कर एक चतुर्भुज बनाते हैं। लिली फूल का चित्र है, जिसकी छह पंखुड़ियों के सिरे जुड़कर एक षट्कोण बनाते हैं।
(i) White trillium - Triangle
(ii) Periwinkle - Pentagon
(iii) Morning meadow - Quadrilateral
(iv) Lily - Hexagon
In simple words: This question explores how polygons can be observed in nature, specifically by connecting the tips of flower petals, demonstrating triangular, pentagonal, quadrilateral, and hexagonal shapes.

🎯 Exam Tip: This question tests observation skills and the ability to identify geometric shapes in natural patterns. Accurate drawing and correct polygon naming are key.

Question 5. Draw any polygon and divide it into triangular parts as shown here. Thus work out the sum of the measures of the angles of the polygon.
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक षट्कोण का चित्र है जिसे एक शीर्ष से उसके सभी गैर-संलग्न शीर्षों तक रेखाएँ खींचकर चार त्रिभुजाकार भागों में विभाजित किया गया है।
Hexagon ABCDEF can be divided in 4 triangles namely ΔBAF, ΔBFE, ΔBED and ΔBCD
Sum of the measures of the angles of a triangle = 180°
∴ Sum of measures of the angles of the polygon ABCDEF = Sum of the measures of all the four triangles
= 180° + 180° + 180°+ 180°
= 720°
∴ The sum of the measures of the angles of the given polygon (hexagon) is 720°.
In simple words: A polygon can be divided into triangles by drawing diagonals from one vertex. The sum of the interior angles of the polygon is equal to the sum of the angles of all these triangles. For a hexagon, it can be divided into 4 triangles, so the sum of its angles is 4 times 180 degrees, which is 720 degrees.

🎯 Exam Tip: Understanding that an n-sided polygon can be divided into (n-2) triangles from a single vertex is key. The sum of its interior angles is then (n-2) × 180°.

Maharashtra Board Class 6 Maths Chapter 16 Quadrilaterals Practice Set 38 Intext Questions And Activities

Question 1. From your compass boxes, collect set squares of the same shapes and place them side by side in all possible different ways. What figures do you get? Write their names. (Textbook pg. no. 85)
a. Two set squares
b. Three set squares
c. four set squares
Answer:
a. Two set squares
ℹ️ चित्र व्याख्या (Diagram Explanation): दो सेट स्क्वायर का चित्र है, जिन्हें एक साथ रखकर एक वर्ग बनाया गया है। दो सेट स्क्वायर का चित्र है, जिन्हें एक साथ रखकर एक सामान्य चतुर्भुज बनाया गया है। दो सेट स्क्वायर का चित्र है, जिन्हें एक साथ रखकर एक आयत बनाया गया है। दो सेट स्क्वायर का चित्र है, जिन्हें एक साथ रखकर एक और सामान्य चतुर्भुज बनाया गया है।
Square
Quadrilateral
Rectangle
Quadrilateral
b. Three set squares
ℹ️ चित्र व्याख्या (Diagram Explanation): तीन सेट स्क्वायर का चित्र है, जिन्हें एक साथ रखकर एक चतुर्भुज बनाया गया है। तीन सेट स्क्वायर का चित्र है, जिन्हें एक साथ रखकर एक और चतुर्भुज बनाया गया है।
Quadrilateral
Quadrilateral
c. four set squares
ℹ️ चित्र व्याख्या (Diagram Explanation): चार सेट स्क्वायर का चित्र है, जिन्हें एक साथ रखकर एक आयत बनाया गया है। चार सेट स्क्वायर का चित्र है, जिन्हें एक साथ रखकर एक चतुर्भुज बनाया गया है। चार सेट स्क्वायर का चित्र है, जिन्हें एक साथ रखकर एक और चतुर्भुज बनाया गया है। चार सेट स्क्वायर का चित्र है, जिन्हें एक साथ रखकर एक और चतुर्भुज बनाया गया है।
Rectangle
Quadrilateral
Quadrilateral
Quadrilateral
In simple words: By arranging two, three, or four set squares in different ways, various polygons can be formed, including squares, rectangles, and different types of quadrilaterals. This demonstrates the versatility of basic geometric tools.

🎯 Exam Tip: This activity promotes hands-on learning and spatial reasoning. Understanding how simple shapes combine to form complex ones is a valuable skill in geometry.

Question 2. Kaprekar Number. (Textbook pg. no. 86)
i. Take any 4-digit number in which all the digits are not the same.
ii. Obtain a new 4-digit number by arranging the digits in descending order.
iii. Obtain another 4-digit number by arranging the digits of the new number in ascending order.
iv. Subtract the smaller of these two new numbers from the bigger number. The difference obtained will be a 4-digit number. If it is a 3-digit number, put a 0 in the thousands place. Repeat the above steps with the difference obtained as a result of the subtraction.
v. After some repetitions, you will get the number 6174. If you continue to repeat the same steps you will get the number 6174 every time. Let us begin with the number 8531.
8531 → 7173 → 6354 → 3087 → 8352 → 6174 → 6174
This discovery was made by the mathematician, Dattatreya Ramchandra Kaprekar. That is why the number 6174 was named the Kaprekar number.
Answer:

In simple words: The Kaprekar process involves taking a 4-digit number (with at least two different digits), arranging its digits in descending and ascending order, then subtracting the smaller number from the larger one. Repeating this process always leads to the number 6174, which is known as Kaprekar's Constant.

🎯 Exam Tip: Understanding the steps of the Kaprekar process is key. The number 6174 is a specific mathematical curiosity, so recall its significance if asked about. Ensure subtraction is performed accurately at each step.