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Mensuration Formulas

The document discusses geometric shapes and their properties. It provides formulas for calculating the area and perimeter of rectangles, squares, parallelograms, triangles, trapezoids, circles, semicircles, and sectors. It also gives the surface area and volume formulas for cylinders, cones, spheres, pyramids, cuboids, cubes, and hemispheres.

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ayesha.siiddiquii
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306 views2 pages

Mensuration Formulas

The document discusses geometric shapes and their properties. It provides formulas for calculating the area and perimeter of rectangles, squares, parallelograms, triangles, trapezoids, circles, semicircles, and sectors. It also gives the surface area and volume formulas for cylinders, cones, spheres, pyramids, cuboids, cubes, and hemispheres.

Uploaded by

ayesha.siiddiquii
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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MENSURATION

PYTHAGORAS’ THEOREM

For all the right angled triangles “ the square on the hypotenuse is equal to the
sum of the squares on the other two sides”
𝑐 2 = 𝑎2 + 𝑏 2

𝒄 = 𝑎2 + 𝑏 2 𝒃 = 𝑐 2 − 𝑎2 𝒂 = 𝑐 2 − 𝑏2

Area and Perimeter:


Figure Diagram Area Perimeter
Rectangle
b Area = l × b perimeter = 2( 𝑙 + 𝑏 )

l
Square a

a a
Area = side × side perimeter = 4 × side
a = a×a =4×a

Parallelogram Area = b × h

perimeter = 2(a + b )

Area = ab sin 𝜃
where a, b are sides and 𝜃 is
the included angle
Triangle
1
Area = × 𝑏𝑎𝑠𝑒 × 𝑕𝑒𝑖𝑔𝑕𝑡
2

1
Area = 2 𝑎𝑏 𝑠𝑖𝑛 𝐶 perimeter = a + b + c

= 𝑠 𝑠 − 𝑎 𝑠 − 𝑏 (𝑠 − 𝑐)
𝑎+𝑏+𝑐
where s =
2

____________________________________________________________________________________
Trapezium
perimeter = Sum of all
1
Area = 2 𝑎 + 𝑏 𝑕 sides

Circle
r
Area =  r2 circumference = 2  r

Semicircle 1 2 1
Area = r perimeter =  d + d
r 2 2
Sector 𝑟  
Area =  r  360 length of an arc = 2 r 
2

𝜃 360

Surface Area and Volume:


Figure Diagram Surface Area Volume
Cylinder
Volume =  r h
2
curved surface area = 2πrh
total surface area = 2πr(h + r)

Cone curved surface area = 𝜋𝑟𝑙 1 2


Volume = πr h
where l = (r 2  h 2 ) 3
total surface area = 𝜋𝑟(𝑙 + 𝑟)

Sphere 4 3
Volume = πr
Surface area = 4πr2 3

Pyramid 1
Volume = × base area ×
Base area + area of the shapes in 3
the sides perpendicular height

Cuboid

Surface area = 2(𝑙𝑏 + 𝑏𝑕 + 𝑙𝑕) Volume = 𝑙 × 𝑏 × 𝑕

Cube
Surface area = 6𝑙 2 Volume = 𝑙 3

2 3
Hemisphere Curved surface area = = 2 r2 Volume = r
3

____________________________________________________________________________________

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