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Mensuration
AREA AND PERIMETER
1. Triangle
(a) Perimeter (2s) = a + b + c
(b) Area s s a s b s c c
b
1 height
(c) Area u base u height where a, b, c are sides
2
a
abc base
of the triangle and S is semi-perimeter, S
2
2. Right-angled triangle
(a) Perimeter = b + p + h
1
(b) Area = u b u p p
2 h
(c) Hypotenuse (h) = b 2 p 2
where b base, p perpendicular, h hypotenuse b
3. Right-angle Isosceles triangle
(a) Hypotenuse = a 2 a 2 2a
2a
(b) Perimeter = 2a 2a a
1 1 1 2
(c) Area = u base u height uaua a
2 2 2
a
4. Equilateral triangle
(a) Perimeter = 3a
3 a a
(b) Height a h
2
3 2
(c) Area a a
4
5. Rectangle
(a) Perimeter = 2 (l+ b)
b
(b) Diagonal = l 2 b2
(c) Area = l u b
l
6. Square a
(a) Perimeter = 4a
(b) Diagonal (d) = 2a a a
a
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1 2
(c) Area = a 2 d
2
7. Parallelogram
(a) Perimeter = 2 (a + b) h b
(b) Area = Base u Height
a
8. Rhombus
1
(a) Side = d12 d 22 d1
2
(b) Perimeter = 2 d12 d 22
d2
1
(c) Area = d1d 2
2
b
9. Trapezium
1 c
(a) Area = a b uh h d
2
(b) Perimeter = a + b + c + d
a
10. Quadrilateral C
c
1 D
(a) Area = u AC u h1 h2
2 h1 b
d h2
(b) Perimeter = a + b + c + d
A a B
11. Circle
(a) Diameter (d) = 2r
(b) Circumference 2S r Sd
Sd2
(c) Area = S r 2
4 r
Sr 2
(d) Area of semi-circle =
2
Sr 2
(e) Area of quadrant =
4
12. Sector
T 1
(a) Area of sector (A) = uS r2 lr r
360 2
T r T
(b) Length of arc (l) = u 2S r
360
13. Regular Polygon l
1
(a) Area = number of sides u radius of the inscribed circle
2
§n2·
(b) Vertex angle of a regular polygon T ¨ ¸ u180q
© n ¹
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14. Volume and Surface Area
(i) Cuboid
(a) Volume = l u b u h
(b) Surface Area = 2 lb bh hl h
(c) Diagonal = l 2 b 2 h 2
b
(d) Area of four walls = 2 l b u h
l
(ii) Cube
(a) Volume = a 3
(b) Surface Area = 6a 2
a
(c) Diagonal = 3a
a
a
(iii) Right Circular Cylinder
(a) Volume = S r 2 h
(b) Curved Surface Area 2S rh h
(c) Total Surface Area = 2S r r h
(d) Area of each end or base area = S r 2
r
(iv) Right Circular Cone
1
(a) Volume = S r 2 h
3
l
(b) Slant height = r 2 h 2 h
(c) Curved Surface Area = S rl
(d) Base Area = S r 2 r
(e) Total Surface Area = S r r l
(v) Sphere
4 3 r
(a) Volume = Sr
3
(b) Total Surface Area = 4S r 2
(vi) Hemisphere
2 3
(a) Volume = Sr
3 r
(b) Total surface area = 3S r 2
(c) Curved Surface Area = 2S r 2
h
(d) Spherical Gap of Radius ‘r’ and Height ‘h’
Volume 1/ 3S h 2 3r h r O
Surface area 2 S rh
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(vii) Frustum of Cone
2
(a) Slant height (l) h2 R r r
Sh
(b) Volume (V) = R 2 r 2 Rr h l
3
(c) Curved Surface Area = S R r l R
(d) Total Surface Area = S ª¬ R r
2 2
l R r º¼
(viii) Prism and Pyramid
A. Prism
(a) Volume of a Right Prism = Area of the base u Height
(b) Lateral Surface Area = Perimeter of the Base u Height
B. Pyramid
1 O
(a) Volume of a Pyramid = u Area of the base u height
3
(b) The whole surface area of a Pyramid is the sum of the
areas of the base and the lateral surface areas.
D
C
E
Q P
A B
