# Mensuration ## Mensuration

### 3. Mensuration

#### 3.1 – Area

• Area of a Rectangle:
• Length × Width
• l × w
• Area of  Trapezium:
• ½ (Base+ 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