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Area
Area of a Triangle
Used when a triangle has a base and a height.
A = ½ × b × h
Circle
Circumference of a Circle
The circumference is the distance around the circle.
C = 2πr
Volume
Volume of a Cube
A cube has equal side lengths.
V = a³
Surface Area
CSA of a Cylinder
CSA means the curved surface only, not the top and bottom.
CSA = 2πrh
Area of a Triangle
Use half times base times height. The height must be perpendicular to the base.
Solved Examples
Example 1: base = 12 cm, height = 8 cm
- Write the formula: A = ½ × b × h.
- Substitute: A = ½ × 12 × 8.
- Calculate: A = 48 cm².
Example 2: base = 10 cm, height = 9 cm
- A = ½ × b × h.
- A = ½ × 10 × 9.
- A = 45 cm².
Example 3: base = 16 cm, height = 7 cm
- A = ½ × b × h.
- A = ½ × 16 × 7.
- A = 56 cm².
Auto-Checked Practice
Circumference of a Circle
Circumference means the distance around the circle. Use C = 2πr.
Solved Examples
Example 1: radius = 7 cm
- Formula: C = 2πr.
- Substitute: C = 2 × 22/7 × 7.
- Calculate: C = 44 cm.
Example 2: radius = 5 cm
- C = 2πr.
- C = 2 × 3.14 × 5.
- C = 31.4 cm.
Example 3: radius = 10 cm
- C = 2πr.
- C = 2 × 3.14 × 10.
- C = 62.8 cm.
Auto-Checked Practice
Volume of a Cube
A cube has equal sides. To find volume, multiply the side by itself three times.
Solved Examples
Example 1: side = 5 cm
- Formula: V = a³.
- Substitute: V = 5³.
- Calculate: V = 125 cm³.
Example 2: side = 4 cm
- V = a³.
- V = 4³.
- V = 64 cm³.
Example 3: side = 6 cm
- V = a³.
- V = 6³.
- V = 216 cm³.
Auto-Checked Practice
Curved Surface Area of a Cylinder
CSA means only the curved side of the cylinder. Do not include the top and bottom circles.
Solved Examples
Example 1: r = 3 cm, h = 10 cm
- Formula: CSA = 2πrh.
- Substitute: CSA = 2 × 3.14 × 3 × 10.
- Calculate: CSA = 188.4 cm².
Example 2: r = 4 cm, h = 8 cm
- CSA = 2πrh.
- CSA = 2 × 3.14 × 4 × 8.
- CSA = 200.96 cm².
Example 3: r = 5 cm, h = 12 cm
- CSA = 2πrh.
- CSA = 2 × 3.14 × 5 × 12.
- CSA = 376.8 cm².