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Mensuration: Top Careers & You

1. The document provides formulas for calculating the perimeters and areas of various geometric shapes including rectangles, squares, parallelograms, rhombuses, quadrilaterals, trapezoids, triangles, circles, semicircles, and sectors of circles. 2. It also lists formulas for calculating the lateral/curved surface areas and volumes of solids like cuboids, cubes, cylinders, cones, spheres, and hemispheres. 3. The shapes and solids covered include their defining properties like side lengths, radii, heights, and angles.

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shekhar.mnnit
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99 views4 pages

Mensuration: Top Careers & You

1. The document provides formulas for calculating the perimeters and areas of various geometric shapes including rectangles, squares, parallelograms, rhombuses, quadrilaterals, trapezoids, triangles, circles, semicircles, and sectors of circles. 2. It also lists formulas for calculating the lateral/curved surface areas and volumes of solids like cuboids, cubes, cylinders, cones, spheres, and hemispheres. 3. The shapes and solids covered include their defining properties like side lengths, radii, heights, and angles.

Uploaded by

shekhar.mnnit
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 4

Top Careers & You

_________________________________________________________________________________________________

MENSURATION
AREA
Areas of some well-known figures are given below:

S.
No.

Name

1.

Rectangle

Figure

Perimeter in
units of
length

Area in square
units

2(a + b)

ab

4a

a2

b
a

a = length
b = breadth
a

2.

Square

a = side

1
2
(diagonal)
2
a

3.

Parallelogram

b
a

a = side
b = side adjacent to a
h = distance between the
opp. parallel sides

2(a + b)

ah

4a

1
d1d2
2

Sum of its four


sides

1
(AC) (h1 + h2)
2

a
d1
a

d2

Rhombus
a

a = side of rhombus; d1,d2


are the two diagonals

4.

D
h1
h2

Quadrilateral

AC is one of its diagonals


and h1, h2 are the
altitudes on AC from D, B
respectively.

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b
h

6.

Trapezium

a, b, are parallel sides


and h is the distance
between parallel sides
a

Triangle

1
h(a + b)
2

h
b

7.

Sum of its four


sides

b is the base and h is


the altitude.
a, b, c are three sides

a + b + c = 2s
where s is the
semi perimeter.

1
bh
2
or
s(s a)(s b) (s c)

of .

8.

Right triangle

b+h+d

1
bh
2

d(hypotenuse)
b 2 + h2

9.

Equilateral
triangle

h
a

3
a
2

h = altitude =

10.

1
ah
2

(ii)

3 2
a
4

3a

a = side

Isosceles
triangle

(i)

2a + c

c 4a 2 c 2
4

2a + d

1 2
a
2

c = unequal side
a = equal side
d

11.

d(hypotenuse)
Isosceles
right triangle

=a 2

a = Each of equal
sides.
The angles are 90o,
45o, 45o.
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12.

Circle

2r

r2

r + 2r

1 2
r
2

r = radius of the circle


=

13.

22
or 3.1416
7

Semicircle

r = radius of the circle

l + 2r

14.

Sector of a
circle

l
o
= central angle of the

sector
r = radius of the sector
l = length of the arc

where l =

2r
360

r2
360

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VOLUME

S.
No

Nature
of the

Shape of the solid

solid

Lateral/

Total surface

curved

area

Volume

surface area
h

1.

Cuboid

2h (l + b)

2(lb + bh + lh)

lbh

l = length
a

2.

Cube

4a2

6a2

a3

2rh

2r(r + h)

r2h

r l

r(l + r)

1 2
r h
3

4r2

4 3
r
3

2r2

3r2

2 3
r
3

a
a

a = edge
r

3.

Right
circular
cylinder

h
r

r = radius of base
h = height of the
cylinder
l

4.

Right
circular
cone

h = height
r = radius
l = slant height

5.

Sphere
r = radius
r

6.

Hemisphere

r = radius

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