These NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area InText Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area InText Questions
NCERT In-text Question Page No. 205
Question 1.
What would you need to find, area or
perimeter, to answer the following?
1. How much space does a blackboard occupy?
2. What is the length of a wire required to fence a rectangular flower bed?
3. What distance would you cover by taking two rounds of a triangular park?
4. How much plastic sheet do you need to cover a rectangular swimming pool?
Answer:
1. Area 2.Perimeter 3. Perimeter 4. Area
NCERT In-text Question Page No. 206
Question 1.
Experiment with several such shapes and cutouts. You might find it useful to draw these shapes on squared sheets and compute their areas and perimeters. You have seen that increase in perimeter does not mean that area will also increase.
Answer:
Please do this question yourself with the help of your subject teacher.
Question 2.
Give two examples where the area increases as the perimeter increases.
Answer:
Please do this question yourself with the help of your subject teacher.
Question 3.
Give two examples where the area does not increase when perimeter increases.
Ans: Please do this question yourself with the help of your subject teacher.
NCERT In-text Question Page No. 210
Question 1.
Each of the following rectangles of length 6 cm and breadth 4 cm is composed of congruent polygons. Find the area of each polygon.
Answer:
∴ Length of the rectangle (l) = 6 cm
Breadth of the rectangle (b) = 4 cm
∴ Area of the rectangle = (l x b)
= 6 x 4 cm2 = 24 cm2
(i) Here, number of congruent polygons = 6
∴ Area of each polygon = \(\frac{24}{6}\) cm2 = 4 cm2
(ii) Here, number of congruent polygons = 4
Area of each polygon = \(\frac{24}{4}\)cm2 = 6 cm2
(iii) Here, number of congruent polygons = 2
∴ Area of each polygon = \(\frac{24}{2}\)cm2 = 12 cm2
(iv) Number of congruent polygons = 2
∴ Area of each polygon = \(\frac{24}{2}\)cm2 = 12 cm2
(v) Number of congruent polygons = 8
∴ Area of each polygon = \(\frac{24}{8}\)cm2 = 3 cm2
NCERT In-text Question Page No. 212
Question 1.
Find the area of the following parallelograms:
(iii) In a parallelogram ABCD, AB = 7.2 cm and the perpendicular from C on AB is 4.5 cm.
Answer:
(i) Base = 8 cm, Height = 3.5 cm
∴ Area of the parallelogram = Base x
Height = 8 cm x 3.5 cm = 28 cm2
(ii) Base = 8 cm, Height = 2.5 cm
Area of the parallelogram = Base x Height = 8 cm x 2.5 cm = 20 cm2
(iii) Base of parallelogram ABCD = (AB) = 7.2 cm
Height of parallelogram ABCD = 4.5 cm
Area of parallelogram ABCD
= Base x Height
= 7.2 cm x 4.5 cm = \(\frac { 72 }{ 10 }\)cm x \(\frac { 45 }{ 10 }\)cm
= \(\frac{3240}{100}\) cm2 = 32.40 cm2
NCERT In-text Question Page No. 213
Question 1.
Try the activity given on page 213, NCERT Textbook with different types of triangles.
Answer:
Do it yourself.
Question 2.
Take different parallelograms. Divide each of the parallelograms into two triangles by cutting any of its diagonals. Are the triangles congruents.
Answer:
Do it yourself.
NCERT In-text Question Page No. 219
Question 1.
In the adjoining figure,
(a) Which square has the larger perimeter?
(b) Which is larger, perimeter of smaller square or the circumference of the circle?
Answer:
(a) The outer square has the larger perimeter.
(b) The circumference of the circle is larger than the perimeter of the smaller square.
NCERT In-text Question Page No. 222
Question 1.
Draw circles of different radii on a graph paper. Find the drea by counting the number of squares. Also find the area by using the formula. Compare the two answers.
Answer:
Do it yourself.
NCERT In-text Question Page No. 225
Question 1.
Convert the following:
(i) 50 cm2 in mm2
(ii) 2 ha in m2
(iii) 10 m2 in cm2
(iv) 1000 cm2 in m2
Answer:
(i) 50 cm2 in mm2
∵ 1 cm2 = 100 mm2
∴ 50 cm2 = 50 x 100 mm2 = 5000 mm2
(ii) 2 ha in m2
1 ha = 1000 m2
∴ 2 ha = 2 x 1000 m2 = 20000 m2
(iii) 10 m2 in cm2
∵ 1 cm2 = 10000 cm2
∴ 10 m2= 10 x 10000 cm2 = 100000 cm2
(iv) 1000 cm2 in m2
∵ 10000 cm2 = 1 m2
∴ 1 cm2 = \(\frac{1}{10000}\) m2
So, 1000 cm2 = \(\frac{1}{10000}\) x 1000 m2
= \(\frac{1}{10}\) m2 = 0.1m2