9th Standard CBSE Syllabus & Materials
9th Standard CBSE
CBSE 9th Standard Mathematics Statistics Sample Question Papers Study Material - QB365 Set D
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CBSE 9th Standard Mathematics Statistics Sample Question Papers Study Material - QB365 Set C
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CBSE 9th Standard Mathematics Statistics Sample Question Papers Study Material - QB365 Set B
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CBSE 9th Standard Mathematics Statistics Sample Question Papers Study Material - QB365 Set A
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CBSE 9th Standard Mathematics Surface Areas and Volumes Sample Question Papers Study Material - QB365 Set D
NEW9th Standard CBSE
CBSE 9th Standard Mathematics Surface Areas and Volumes Sample Question Papers Study Material - QB365 Set C
Published on: 29/10/2025
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1.
Area of a triangle =
\(\frac { 1 }{ 2 } \times\) Base \( \times\) Height
Base \( \times\) Height
\(\frac { 1 }{ 3} \times\) Base \( \times\) Height
\(\frac { 1 }{ 4 } \times\) Base \( \times\) Height
2.
Base of a triangle =
\(\frac { 2\times Area }{ Height } \)
\(\frac { Area }{ Height } \)
\(\frac { Area }{ 2\quad Height } \)
\(\frac { Area }{ 4\quad Height } \)
3.
Height of a triangle =
\(\frac { 2\times Area }{ Base } \)
\(\frac { Area }{ Base } \)
\(\frac { Area }{ 3 \quad Base } \)
\(\frac { Area }{ 4 \quad Base } \)
4.
The area of \(\triangle \)ABC in which AB = BC = 4 cm and \(\angle B=90°\) is
16 cm2
8 cm2
4 cm2
12 cm2
5.
Area of a triangle having base 6 cm and altitude 8 cm is
48 cm2
24 cm2
64 cm2
36 cm2
6.
The base and hypotenuse of a right triangle are respectively 6 cm and 10 cm long.Its area is
60 cm2
120 cm2
30 cm2
24 cm2
7.
Area of a triangle is 60 cm2.Its base is 15 cm.Its altitude is
30 cm
4 cm
8 cm
10 cm
8.
The area of a right triangle is 36 cm2 and its base is 9 cm.Find the length of the perpendicular.
8 cm
4 cm
16 cm
32 cm
9.
The side of an isosceles right triangle of hypotenuse \(5\sqrt { 2 } \) cm is
10 cm
8 cm
5 cm
\(3\sqrt { 2 } \) cm
10.
The base of a right triangle is 15 cm and its hypotenuse is 25 cm.Then its area is
187.5 cm2
375 cm2
150 cm2
300 cm2
11.
Area of an isosceles right triangle is 8 cm2.Its hypotenuse is
\(\sqrt { 32 } \) cm
4 cm
\(4\sqrt { 3 } \) cm
\(2\sqrt { 6 } \) cm
12.
Side of an equilateral triangle is 4 cm. Its area is
\(4\sqrt { 3 } \) cm2
\(\frac { \sqrt { 3 } }{ 4 } \) cm2
\(\sqrt { 3 } \) cm2
\(2\sqrt { 3 } \) cm2
13.
The area of an equilateral triangle with side Area \(4\sqrt { 3 } \) cm is (\(\sqrt { 3 } \) = 1.732)
20 cm2
20 \(\sqrt { 3 } \) cm2
18.784 cm2
20.784 cm2
14.
The side of an equilateral triangle is 6 cm.The area of the triangle is
\(6\sqrt { 3 } \) cm2
\(9\sqrt { 3 } \) cm2
\(16\sqrt { 3 } \) cm2
\(3\sqrt { 3 } \) cm2
15.
Find the length of the side of an equilateral triangle whose area is \(9\sqrt { 3 } \)cm2.
1 cm
2 cm
3 cm
6 cm
16.
The area of an equilateral triangle is \(16\sqrt { 3 } \) m2.Its perimeter (in meters) is
12
48
24
306
17.
In an equilateral triangle of side 'a', the length of the altitude is
\(\frac { \sqrt { 3 } { a } }{ 4 } \)
\(\frac { \sqrt { 3 } { a } }{ 2 } \)
\({ \sqrt { 3 } { a } }\)
\(2{ \sqrt { 3 } { a } }\)
18.
The perimeter of an equilateral triangle is 60 m.Its area is
\(10\sqrt { 3 } \) m2
\(100\sqrt { 3 } \)m2
\(15\sqrt { 3 } \)m2
\(20\sqrt { 3 } \)m2
19.
If the length of median of an equilateral triangle be x cm, then its area is
\({ x }^{ 2 }\)
\(\frac { \sqrt { 3 } }{ 2 } { x }^{ 2 }\quad \)
\(\frac { { x }^{ 2 } }{ \sqrt { 3 } } \)
\(\frac { { x }^{ 2 } }{ 2 } \)
20.
The area of a triangular figure whose sides are 11 cm, 60 cm, and 61 cm is
165 cm2
330 cm2
160 cm2
320 cm2
21.
The sides of a triangle are 7 cm, 24 cm, and 25 cm.Its area is
168 cm2
84 cm2
87.5 cm2
300 cm2
22.
The diagonals of a rhombus are 10 cm and 8 cm.Its area is
80 cm2
40 cm2
9 cm2
36 cm2
23.
Find the area of a quadrilateral whose one diagonal is 8 cm and the sum of perpendiculars from vertices is 10 cm.
20 cm2
40 cm2
80 cm2
160 cm2
24.
The edges of a triangular board are 6 cm, 8 cm, and 10 cm.The cost of painting it at the rate of 9 paise per cm2 is
Rs. 2.00
Rs. 3.00
Rs. 2.16
Rs. 2.48
25.
If s is the semiperimeter of a \(\Delta \) ABC whose sides are a, b, c, then s=
a+b+c
\(\frac { a+b+c }{ 2 } \)
\(\frac { a+b+c }{ 3 } \)
\(\frac { a+b+c }{ 4 } \)
26.
Area of an equilateral triangle of side a is
\(\frac { \sqrt { 3 } { a }^{ 2 } }{ 4 } \)
\(\frac { a\sqrt { 3 } }{ 4 } \)
\(\sqrt { 3 } { a }^{ 2 }\)
\(a\sqrt { 3 } \)
27.
Heron's formula is
\(\Delta =\sqrt { s(s+a)(s+b)(s+c) } \)
\(\Delta =\sqrt { s(s-a)(s-b)(s-c) } \)
\(\Delta =\sqrt { s(s-a)(s-b)(s-c) } \), s=a+b+c
\(\Delta =\sqrt { s(s-a)(s-b)(s-c) } \), 2s=a+b+c
28.
The area of an isosceles triangle whose base is 'a' and equal sides are of length 'b' is
\(\frac { a }{ 4 } \sqrt { 4{ b }^{ 2 }-{ a }^{ 2 } } \)
\(\frac { b }{ 4 } \sqrt { 4{ b }^{ 2 }-{ a }^{ 2 } } \)
\(\frac { b }{ 2 } \sqrt { 4{ b }^{ 2 }-{ a }^{ 2 } } \)
\(\frac { a }{ 2 } \sqrt { 4{ b }^{ 2 }-{ a }^{ 2 } } \)
29.
Area of an equilateral triangle of side 'a' units can be calculated by using the formula
\(\sqrt { { s }^{ 2 }{ (s-a) }^{ 2 } } \)
(s-a)\(\sqrt { { s }^{ 2 }{ (s-a) } } \)
\(\sqrt { { s }{ (s-a) }^{ 2 } } \)
(s-a)\(\sqrt { { s }{ (s-a) } } \)
30.
Find the perimeter of the triangle whose sides are 17 cm, 33 cm, and 20 cm.
70 cm
50 cm
53 cm
37 cm
31.
Find the semiperimeter of the triangle whose sides are 21 cm, 20 cm, and 29 cm.
35 cm
70 cm
41 cm
50 cm
32.
The semiperimeter of a triangle having the length of its sides as 20 cm, 15 cm, and 9 cm is
44 cm
21 cm
22 cm
None
33.
The perimeter of a triangular plot is 16 m.If the measures of its two sides are 5 m, and 6m, then find the third side.
2 m
3 m
5 m
4 m
34.
The difference of semi-perimeter and the sides of \(\Delta \) ABC are 8 cm, 7 cm, and 5 cm respectively.Its semi-perimeter is
10 cm
5 cm
15 cm
20 cm
35.
Two sides of a triangle are 13 cm, and 14 cm and its semi-perimeter is 18 cm.Then third side of the triangle is
12 cm
11 cm
10 cm
9 cm
36.
The area of a triangle whose sides are 13 cm, 14 cm, and 15 cm is
42 cm2
86 cm2
84 cm2
100 cm2
37.
The sides of a triangle 40 cm, 70 cm, and 90 cm.The area of the triangle is
\(600\sqrt { 5 } \)cm2
\(500\sqrt { 6 } \) cm2
\(482\sqrt {5 } \) cm2
\(60\sqrt {5 } \) cm2
38.
Two equal sides of an isosceles triangle are 13 cm each and its perimeter is 36 cm.Find the area of the triangle.
20 cm2
30 cm2
40 cm2
60 cm2
39.
Find the area of an isosceles triangle whose equal sides are 6 cm each and the third side is 8 cm.
\(8\sqrt { 5 } \) cm2
\(5\sqrt { 8 } \) cm2
\(3\sqrt { 55 } \) cm2
\(3\sqrt { 8 } \) cm2
40.
The area of an isosceles triangle is 12 cm2 .The lengths of its equal sides are 5 cm each.Find its base.
5 cm
3 cm
4 cm
6 cm or 8 cm
41.
The perimeter of a triangle is 36 cm and its are in the ratio a:b:c=3:4:5 then a,b,c are respectively
9 cm, 15 cm, 12 cm
15 cm, 12 cm, 9 cm
12 cm, 9 cm, 15 cm
9 cm, 12 cm, 15 cm
42.
The sides of a triangular plot are in the ratio 4:5:6 and its perimeter is 150 cm.Then the sides are
4 cm, 5 cm, 6 cm
40 cm, 50 cm, 60 cm
8 cm, 10 cm, 12 cm
120 cm, 150 cm, 180 cm
43.
The sides of a triangular field are in the ratio 3:4:5.The perimeter of the triangular field is 144 m.Find the longest side of the field.
15 m
30 m
60 m
90 m
44.
The sides of a triangular park are in the ratio 25: 17: 12 and its perimeter is 540 m. Find the smallest side of the park.
60 m
120 m
90 m
45 m
45.
1 hectare =
10 m2
100 m2
1000 m2
10000 m2
46.
1 are =
10 m2
100 m2
1000 m2
10000 m2
47.
Find the area of a right-angled triangle, if the radius of the semi-circle is 3 cm and altitude drawn to the hypotenuse is 2 cm.
4 cm2
6 cm2
8 cm2
12 cm2
48.
The side of a square is 5 cm.Its perimeter is
5 cm
20 cm
25 cm
10 cm.
49.
If the area of a square is 625 ares, then its perimeter is
250 m
500 m
1000 m
25 m
50.
Area of a rhombus is 90 cm2 .One of its diagonals measures 10 cm.Length of the other diagonal is
18 cm
36 cm
80 cm
9 cm
51.
The area of a rhombus is 96 cm2.If one of its diagonals is 16 cm, then the length of its sides is
12 cm
10 cm
8 cm
6 cm
52.
The parallel sides of a trapezium are 32 cm and 20 cm and the distance between them is 15 cm.Find the area of the trapezium.
290 cm2
390 cm2
390 m2
400 m2
53.
The perimeter of a rhombus is 20 cm.If one of its diagonals is 6 cm, then its area is
28 cm2
36 cm2
24 cm2
20 cm2
54.
The parallel sides of a trapezium are 45.8 cm and 81.2 cm and the distance between then is 22 cm.Find the area of the trapezium.
1397 cm2
1937 cm2
3197 cm2
139.7 cm2
55.
My garden is in the form of a trapezium whose parallel sides are 20 m and 16 m long respectively and the distance between them is 12 m.How much manure do I require for my garden if 1 m2 requires 200 g of manure?
43.2 kg
86.4 kg
21.6 kg
None of these
56.
A regular hexagon has a side 8 cm. Find its area.
\(=8\sqrt { 3 } \) cm2
\(=96\sqrt { 3 } \) cm2
\(=4\sqrt { 3 } \) cm2
\(=12\sqrt { 3 } \) cm2
57.
The areas of a rectangle and a parallelogram are equal.If the length and breadth of the rectangle are 8 cm and 4.5 cm respectively and the base of the parallelogram is 9 cm, then find the altitude to the base of the parallelogram.
1 cm
2 cm
3 cm
4 cm
58.
In figure, ar (||gm ABCD) is
10 cm
20 cm
\(10\sqrt { 3 } \) cm2
\(20\sqrt { 3 } \) cm2
59.
A square and an equilateral triangle have equal perimeters.If the diagonal of the square is \(12\sqrt { 2 } \) cm then area of the triangle is
\(24\sqrt { 2 } \) cm2
\(24\sqrt { 3 } \) cm2
\(48\sqrt { 3 } \) cm2
\(64\sqrt { 3 } \) cm2
60.
Area of a trapezium =
\(\frac { 1 }{ 2 } \times \) sum of parallel sides \(\times \)distance between the parallel sides
Sum of parallel sides \(\times \)distance between the parallel sides
\(\frac { 1 }{ 3} \times \) sum of parallel sides \(\times \)distance between the parallel sides
None of these
61.
Area of a rhombus =
\(\frac { 1 }{ 2 } \times \) product of diagonals
product of diagonals
\(\frac { 1 }{ 3 } \times \) product of diagonals
\(\frac { 1 }{ 4 } \times \) product of diagonals
62.
Area of a parallelogram =
\(\frac { 1 }{ 2 } \times \)Base \(\times \) Height
Base \(\times \) Height
\(\frac { 1 }{ 4 } \times \)Base \(\times \) Height
\(\frac { 1 }{ 3 } \times \)Base \(\times \) Height
63.
Area of a quadrilateral =
\(\frac { 1 }{ 2 } \times \) a diagonal \(\times \) sum of the perpendicular on the diagonal
a diagonal \(\times \) sum of the perpendicular on the diagonal
\(\frac { 1 }{ 3 } \times \) a diagonal \(\times \) sum of the perpendicular on the diagonal
\(\frac { 1 }{ 4 } \times \) a diagonal \(\times \) sum of the perpendicular on the diagonal
1.
Formula
2.
Formula
3.
Formula
4.
Area = \(\frac { AB\times BC }{ 2 } =\frac { 4\times 4 }{ 2 } \)= 8 cm2
5.
Area = \(\frac { Base\times Perpendicular }{ 2 } =\frac { 6\times 8 }{ 2 } \) = 24 cm2
6.
(d)
24 cm2
7.
(c)
8 cm
8.
\(36=\frac { 9\times Perpendicular }{ 2 } \)
\(\quad \Rightarrow \) Perpendicular = 8 cm.
9.
(c)
5 cm
10.
(c)
150 cm2
11.
(a)
\(\sqrt { 32 } \) cm
12.
Area \(=\frac { \sqrt { 3 } }{ 4 } { a }^{ 2 }=\frac { \sqrt { 3 } }{ 4 } { \left( 4 \right) }^{ 2 }=4\sqrt { 3 } \) cm2
13.
(d)
20.784 cm2
14.
\(\frac { \sqrt { 3 } }{ 4 } { (6) }^{ 2 }=9\sqrt { 3 }\) cm2.
15.
\(\frac { \sqrt { 3 } }{ 4 } { a }^{ 2 }=9\sqrt { 3 } \quad \Rightarrow \) a=6 cm
16.
\(\frac { \sqrt { 3 } { a }^{ 2 } }{ 4 } =16\sqrt { 3 } \quad \Rightarrow \) a=8
Perimeter 3a = 3 \(\times \) 8 = 24 m
17.
(b)
\(\frac { \sqrt { 3 } { a } }{ 2 } \)
18.
Side (a) = \(\frac { 60 }{ 3 } =20\)m
\(\therefore \) Area =\(\quad =\frac { \sqrt { 3 } }{ 4 } { a }^{ 2 }=\frac { \sqrt { 3 } }{ 4 } { (20) }^{ 2 }=100\sqrt { 3 } \) m2
19.
(c)
\(\frac { { x }^{ 2 } }{ \sqrt { 3 } } \)
20.
(b)
330 cm2
21.
\(\because \) 72+242=252
\(\therefore \) Triangle is right angled with hypotenuse 25 cm.
\(\therefore \) Area =\(\frac { 7\times 24 }{ 2 } \)= 84 cm2
22.
Area = \(\frac { 1 }{ 2 } \times 10\times 8=40\)cm2
23.
\(\frac { 1 }{ 2 } \times 8\times 10=40\)cm2
24.
\(\because \) 62+82=102
\(\because \) The triangle is right angled with hypotenuse 10 cm
\(\therefore \) Area \(=\frac { 6\times 8 }{ 2 } \)= 24 cm2
\(\therefore \) Cost of painting =24 \(\times \) 0.09 = Rs. 2.16
25.
Formula
26.
Formula
27.
See Hero's formula.
28.
(a)
\(\frac { a }{ 4 } \sqrt { 4{ b }^{ 2 }-{ a }^{ 2 } } \)
29.
a = b = c
\(\therefore \) Area = \(\sqrt { s(s-a)(s-b)(s-c) } \)
=(s-a)\(\sqrt { { s }{ (s-a) } } \)
30.
Perimeter = 17+33+20 = 70 cm
31.
s=\(\frac { 21+20+29 }{ 2 } \)=35 cm
32.
s=\(\frac { 20+15+9 }{ 2 } \)=22 cm
33.
(c)
5 m
34.
(d)
20 cm
35.
(d)
9 cm
36.
\(s=\frac { a+b+c }{ 2 } =\frac { 13+14+15 }{ 2 } =21\)cm
\(\therefore \) \(\quad =\sqrt { s(s-a)(s-b)(s-c) } \)
\(=\sqrt { 21(21-13)(21-14)(21-15) } =\sqrt { 21\times 8\times 7\times 6 } =84\)cm2
37.
(a)
\(600\sqrt { 5 } \)cm2
38.
(d)
60 cm2
39.
(a)
\(8\sqrt { 5 } \) cm2
40.
(d)
6 cm or 8 cm
41.
a:b:c=3:4:5
a+b+c=12
a=\(\frac { 3 }{ 12 } \times 36\)= 9 cm
b= \(\frac { 4 }{ 12 } \times 36\)=12 cm
c=\(\frac { 5 }{ 12 } \times 36\)=15 cm
42.
4+5+6=15
a:b:c=4:5:6
a=\(\frac { 4 }{ 15 } \times 150\)=40 cm
b=\(\frac { 5 }{ 15 } \times 150\)=50 cm
c=\(\frac { 6 }{ 15 } \times 150\)=60 cm
43.
Longest side = \(\frac { 5 }{ 3+4+5 } \times 144\)=60 m.
44.
Smallest side = \(\frac { 12 }{ 25+17+12 } \times 540\) = 120 m.
45.
Formula
46.
Formula
47.
(b)
6 cm2
48.
Perimeter = 4\(\times \)5=20 cm.
49.
(c)
1000 m
50.
(a)
18 cm
51.
(b)
10 cm
52.
Area = \(\frac { (32+20)\times 15 }{ 2 } \) = 390 cm2
53.
(c)
24 cm2
54.
Area = \(\frac { (45.8+81.2)\times 22 }{ 2 } \)
= 127\(\times \)11 = 1397 cm2
55.
Area = \(\frac { (20+16)\times 12 }{ 2 } \) = 216 m2
\(\therefore \) Manure required = 216\(\times \)200 g = 43.2 kg
56.
Area = 6\(\left\{ \frac { \sqrt { 3 } }{ 4 } { (8) }^{ 2 } \right\} \) = \(96\sqrt { 3 } \) cm2
57.
8\(\times \)4.5 = 9 \(\times \) altitude
\(\Rightarrow \) Altitude = 4 cm
58.
(d)
\(20\sqrt { 3 } \) cm2
59.
(d)
\(64\sqrt { 3 } \) cm2
60.
Formula
61.
Formula
62.
Formula
63.
Formula
9th Standard CBSE Syllabus & Materials
9th Standard CBSE
CBSE 9th Standard Mathematics Surface Areas and Volumes Sample Question Papers Study Material - QB365 Set B
NEW9th Standard CBSE
CBSE 9th Standard Mathematics Surface Areas and Volumes Sample Question Papers Study Material - QB365 Set A
NEW9th Standard CBSE
CBSE 9th Standard Mathematics Heron's Formula Sample Question Papers Study Material - QB365 Set D
NEW9th Standard CBSE
CBSE 9th Standard Mathematics Heron's Formula Sample Question Papers Study Material - QB365 Set C
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