S.chand class 6 Mathematics Chapter 21 Exercise 21A

 Exercise 21A

Question 1

The following shapes are drawn on squared paper. Name each shape.

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Question 2

Fill in the blanks.

(i) A quadrilateral with all sides and all angles equal is a

(ii) A quadrilateral with four equal sides and no right angles can be called a

(iii) A quadrilateral with exactly two sides parallel is a

(iv) The diagonals of this quadrilateral are equal but not perpendicular. The quadrilateral is a

(v) All rectangles, squares and rhombus are , but a trapezium is not.

Question 3

Determine if the given statements are sometimes, always or never true.

(i) A parallelogram is a quadrilateral.

(ii) A parallelogram is a trapezium.

(iii) A rhombus is a square.

(iv) A trapezium is a quadrilateral.

(v) A rectangle is a square.

(vi) A square is a rhombus.

(vii) A square is a rectangle.

(viii) Four sided plane figures are parallelograms.

Question 4

4. Write ' $T$ ' for True or 'F' for false.

(i) Each angle of a rectangle is a right angle.

(ii) The opposite sides of a rectangle are equal in length.

(iii) The diagonals of a square are perpendicular to one another.

(iv) All the sides of a rhombus are of equal length.

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

(vi) The opposite sides of a trapezium are parallel.

Question 5

Give reasons for the following.

(i) A square can be thought of as a special rectangle.

(ii) A rectangle can be thought of as a special parallelogram.

(iii) A square can be thought of as a special rhombus.

(iv) Squares, rectangles, parallelograms are all quadrilaterals.

(v) Square is also a parallelogram.

Multiple Choice Questions (MCQs)

Tick (✔) the correct option.

Question 6

A quadrilateral whose diagonals are equal and bisect each other at right angles is a

(a) parallelogram

(b) rectangle

(c) rhombus

(d) square

Question 7

A quadrilateral-shaped photo-frame has all sides equal. Which of the following is not a possible shape for the photo-frame?

(a) Square

(b) Rectangle

(c) Rhombus

(d) Trapezium

Question 8

A figure is said to be regular, if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral?

(a) Parallelogram

(b) Rhombus

(c) Square

(d) Rectangle.

Question 9

Which quadrilateral is not a parallelogram?

(a) Rectangle

(b) Trapezium

(c) Square

(d) Rhombus

RS Aggarwal solution class 8 chapter 21 Data Handling Exercise 21A

Exercise 21A

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Q1 | Ex-21A | Class 8 | RS AGGARWAL | chapter 21 | Data Handling

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Question 1:

The number of members in 20 families are given below:
4, 6, 5, 5, 4, 6, 3, 3, 5, 5, 3, 5, 4, 4, 6, 7, 3, 5, 5, 7.
Prepare a frequency distribution of the data.

Answer 1:

First, we will arrange the data in increasing order.

3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7

Frequency table of the above data:
 

Number of members	Tally marks	Number of families (frequency)
3	$\left|\right|\left|\right|$	4
4	$\left|\right|\left|\right|$	4
5	$\cancel{\left|\right|\left|\right|}$ $\left|\right|$	7
6	$\left|\right||$	3
7	$\left|\right|$	2
Total		20

Q2 | Ex-21A | Class 8 | RS AGGARWAL | chapter 21 | Data Handling

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Question 2:

A dice was thrown 30 times and the following outcomes were noted:
2, 1, 2, 4, 6, 1, 2, 3, 6, 5, 4, 4, 3, 1, 1, 3, 1, 1, 5, 6, 6, 2, 2, 3, 4, 2, 5, 5, 6, 4.
Prepare a frequency table.

Answer 2:

Arranging the outcomes in increasing order, we get:

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6

Now, we have:

1 was thrown 6 times
2 was thrown 6 times
3 was thrown 4 times
4 was thrown 5 times
5 was thrown 4 times
6 was thrown 5 times

Frequency distribution table of the above data:
 

Number	Tally mark	frequency
1	$\cancel{\left|\right|\left|\right|} |$	6
2	$\cancel{\left|\right|\left|\right|} |$	6
3	$\left|\right|\left|\right|$	4
4	$\cancel{\left|\right|\left|\right|}$	5
5	$\left|\right|\left|\right|$	4
6	$\cancel{\left|\right|\left|\right|}$	5
Total		30

Q3 | Ex-21A | Class 8 | RS AGGARWAL | chapter 21 | Data Handling

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Question 3:

The following data gives the number of children in 40 families:
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.
Represent it in the form of a frequency distribution.

Answer 3:

Arranging the dates in ascending order, we get:

0, 0 ,0 , 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,2,2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6

There are:
4 families with no children
7 families with 1 child
12 families with 2 children
5 families with 3 children
6 families with 4 children
3 families with 5 children
3 families with 6 children

The frequency distribution table for the above data can be generated as below:
 

Number of children	Tally mark	Number of families (frequency)
0	$\left|\right|\left|\right|$	4
1	$\cancel{\left|\right|\left|\right|} \left|\right|$	7
2	$\cancel{\left|\right|\left|\right|} \cancel{\left|\right|\left|\right|} \left|\right|$	12
3	$\cancel{\left|\right|\left|\right|}$	5
4	$\cancel{\left|\right|\left|\right|}$ $|$	6
5	$\left|\right||$	3
6	$\left|\right||$	3
	Total	40