CBSE · NCERT · Class 7 Maths · Chapter 9

NCERT Solutions: Class 7 Maths Chapter 9 - Perimeter and Area

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Chapter-wise NCERT intext questions and exercise answers for Perimeter and Area, grounded in the official textbook.

Questions are taken verbatim from the NCERT textbook; answers were grounded against the chapter's content during generation. Items needing review are marked.
Sections in this chapter
Exercise 9.1 1Exercise 9.2 1
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1Exercise 9.11 questions
Q.1-81. Find the area of each of the following parallelograms: (a) base 7 cm, height 4 cm (b) base 5 cm, height 3 cm (c) base 2.5 cm, height 3.5 cm (d) base 5 cm, height 4.8 cm (e) base 2 cm, height 4.4 cm. 2. Find the area of each of the following triangles: (a) base 4 cm, height 3 cm (b) base 5 cm, height 3.2 cm (c) base 3 cm, height 4 cm (d) base 3 cm, height 2 cm. 3. Find the missing values in the table for parallelograms: (a) base 20 cm, height blank, area $246\text{ cm}^2$ (b) base blank, height 15 cm, area $154.5\text{ cm}^2$ (c) base blank, height 8.4 cm, area $48.72\text{ cm}^2$ (d) base 15.6 cm, height blank, area $16.38\text{ cm}^2$. 4. Find the missing values in the table for triangles: (a) base 15 cm, height blank, area $87\text{ cm}^2$ (b) base blank, height 31.4 mm, area $1256\text{ mm}^2$ (c) base 22 cm, height blank, area $170.5\text{ cm}^2$. 5. PQRS is a parallelogram. QM is the height from Q to SR and QN is the height from Q to PS. If $SR=12$ cm and $QM=7.6$ cm, find: (a) the area of the parallelogram PQRS (b) QN, if $PS=8$ cm. 6. DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD. If the area of the parallelogram is $1470\text{ cm}^2$, $AB=35$ cm and $AD=49$ cm, find the length of BM and DL. 7. $\triangle ABC$ is right angled at A. AD is perpendicular to BC. If $AB=5$ cm, $BC=13$ cm and $AC=12$ cm, find the area of $\triangle ABC$. Also find the length of AD. 8. $\triangle ABC$ is isosceles with $AB=AC=7.5$ cm and $BC=9$ cm. The height AD from A to BC is 6 cm. Find the area of $\triangle ABC$. What will be the height from C to AB i.e., CE?v
Solution

Area of parallelogram $=b\times h$. Area of triangle $=\frac{1}{2}bh$. To find a missing base or height, rearrange the formula.

Answer:

1. (a) $28\text{ cm}^2$ (b) $15\text{ cm}^2$ (c) $8.75\text{ cm}^2$ (d) $24\text{ cm}^2$ (e) $8.8\text{ cm}^2$.
2. (a) $6\text{ cm}^2$ (b) $8\text{ cm}^2$ (c) $6\text{ cm}^2$ (d) $3\text{ cm}^2$.
3. (a) 12.3 cm (b) 10.3 cm (c) 5.8 cm (d) 1.05 cm.
4. (a) 11.6 cm (b) 80 cm (c) 15.5 cm.
5. (a) $91.2\text{ cm}^2$ (b) 11.4 cm.
6. Length of BM = 30 cm; length of DL = 42 cm.
7. Area of $\triangle ABC=30\text{ cm}^2$; length of AD $=\frac{60}{13}$ cm.
8. Area of $\triangle ABC=27\text{ cm}^2$; length of CE = 7.2 cm.

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2Exercise 9.21 questions
Q.1-171. Find the circumference of the circles with the following radius: (Take $\pi=\frac{22}{7}$) (a) 14 cm (b) 28 mm (c) 21 cm. 2. Find the area of the following circles, given that: (a) radius = 14 mm (Take $\pi=\frac{22}{7}$) (b) diameter = 49 m (c) radius = 5 cm. 3. If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet. (Take $\pi=\frac{22}{7}$) 4. A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the cost of the rope, if it costs Rs 4 per meter. (Take $\pi=\frac{22}{7}$) 5. From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Take $\pi=3.14$) 6. Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs Rs 15. (Take $\pi=3.14$) 7. Find the perimeter of the adjoining figure, which is a semicircle including its diameter. The semicircle has diameter 10 cm. 8. Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is Rs $15/\text{m}^2$. (Take $\pi=3.14$) 9. Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take $\pi=\frac{22}{7}$) 10. From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed. Find the area of the remaining sheet. (Take $\pi=\frac{22}{7}$) 11. A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet? (Take $\pi=3.14$) 12. The circumference of a circle is 31.4 cm. Find the radius and the area of the circle? (Take $\pi=3.14$) 13. A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? ($\pi=3.14$) 14. A circular flower garden has an area of $314\text{ m}^2$. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden? (Take $\pi=3.14$) 15. Find the circumference of the inner and the outer circles, shown in the adjoining figure. The outer circle has radius 19 m and the distance from the outer circle to the inner circle along a radius is 10 m, so the inner radius is 9 m. (Take $\pi=3.14$) 16. How many times a wheel of radius 28 cm must rotate to go 352 m? (Take $\pi=\frac{22}{7}$) 17. The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour. (Take $\pi=3.14$)v
Solution

Use circumference $C=2\pi r=\pi d$ and area $A=\pi r^2$. For cost problems, multiply total length or area by the given rate.

Answer:

1. (a) 88 cm (b) 176 mm (c) 132 cm.
2. (a) $616\text{ mm}^2$ (b) $1886.5\text{ m}^2$ (c) $\frac{550}{7}\text{ cm}^2$.
3. 24.5 m; $1886.5\text{ m}^2$.
4. 132 m; Rs 528.
5. $21.98\text{ cm}^2$.
6. 4.71 m; Rs 70.65.
7. 25.7 cm.
8. Rs 30.14 approximately.
9. 7 cm; $154\text{ cm}^2$; 11 cm; circle.
10. $536\text{ cm}^2$.
11. $23.44\text{ cm}^2$.
12. 5 cm; $78.5\text{ cm}^2$.
13. $879.20\text{ m}^2$.
14. Yes.
15. 119.32 m; 56.52 m.
16. 200 times.
17. 94.2 cm.

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