Mensuration
3. Mensuration
3.1 – Area
- Area of a Rectangle:
- Length × Width
- l × w
- Area of 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 theta
- Area of a Parallelogram:
- Base × Height
- b × h
OR
- (b × a) sin theta
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 = theta/360 × 2 × π × radius
which is theta/360 × 2πr
- Sector Area = ᶿ/360 × π × radius²
which is theta/360 × πr²
3.4 – Volume
- Volume of a Prism:
- Volume of a Prism = (area of cross section) × length
which is A × l
- Volume of a Cylinder:
- Volume of a Cylinder = (area of cross section) × length
- Volume of a Cylinder = π × radius² × height
which is πr²h
Volume of a Pyramid:
- Volume of a Pyramid = 1/3 × (base area) × height
which is 1/3 × (A) × h
- Volume of a Cone:
- Volume of a Cone = 1/3 × π × radius² × height
which is 1/3 πr²h
- olume of a Sphere:
- Volume of a Sphere = 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
