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Mensuration Notes

The document provides formulas for calculating the area of various geometric shapes, including rectangles, trapeziums, kites, triangles, parallelograms, and circles. It also outlines the formulas for arc length, sector area, volume of prisms, cylinders, pyramids, cones, and spheres, as well as surface area calculations for cylinders, spheres, and cones. These formulas are essential for mensuration in geometry.

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ezzatahir93
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9 views3 pages

Mensuration Notes

The document provides formulas for calculating the area of various geometric shapes, including rectangles, trapeziums, kites, triangles, parallelograms, and circles. It also outlines the formulas for arc length, sector area, volume of prisms, cylinders, pyramids, cones, and spheres, as well as surface area calculations for cylinders, spheres, and cones. These formulas are essential for mensuration in geometry.

Uploaded by

ezzatahir93
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Mensuration

3.1 – Area
Area of a Rectangle:
Length × Width
l×w

Area of a Trapezium:
½ (Base1 + Base2) × Height
½ (a + b) h

Area of a Kite:
½ (Diagonal1 × Diagonal2)
½ (a × b)

Area of a Triangle:
½ (Base × Height)
½ (b × h)

OR

½ (a × b) sin C

Area of a Parallelogram:
Base × Height
b×h

OR

(b × a) sin θ

3.2 – The Circle


Circumference of a Circle:
Circumference = π × diameter
which is πd
OR

Circumference = 2 × π × radius
which is 2πr

Area of a Circle:
Area = π × radius²
which is πr²

3.3 – Arc Length and Sector Area


Arc Length:
Arc Length = θ/360 × 2 × π × radius
which is θ/360 × 2πr

Sector Area:
Sector Area = θ/360 × π × radius²
which is θ/360 × πr²

3.4 – Volume
Volume of a Prism:
Volume = (area of cross section) × length
which is A × l

Volume of a Cylinder:
Volume = (area of cross section) × length
Volume = π × radius² × height
which is πr²h

Volume of a Pyramid:
Volume = 1/3 × (base area) × height
which is 1/3 × A × h

Volume of a Cone:
Volume = 1/3 × π × radius² × height
which is 1/3 πr²h
Volume of a Sphere:
Volume = 4/3 × π × radius³
which is 4/3 πr³

3.5 – Surface Area


Cylinder:
Curved Surface Area = 2 × π × radius × height
2πrh

Total Surface Area = (2 × π × radius × height) + (2 × π × radius²)


2πrh + 2πr²

Sphere:
Surface Area = 4 × π × radius²
4πr²

Cone:
Curved Surface Area = π × radius × slant height
πrl

Total Surface Area = (π × radius × slant height) + (π × radius²)


πrl + πr²

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