Geometry Formulas

1. Geometry Formulas in Triangles:

The area of a triangle with base b and height h is ½ × (base) × (height), ie. ½ × b × h. The area of an equilateral triangle with length of each side ‘a’ is (√3/4) × a2. Let the lengths of the three sides in a triangle be a, b and c. Then, the properties of sides also called the triangle inequality theorem is:

b – c < a < b + c

a – c < b < a + c

a – b < c < a + b

2. Geometry Formulas in circles:

1. Consider a circle having radius r. Then,

1. Diameter = 2r.

2. Circumference = 2Πr

3. Length of an arc is (θ/360) × 2Πr

4. Area of a sector in the circle is (θ/360) × Πr2

5. Circumference of a semi circle is Πr

6. Perimeter of a semicircle is Πr +2r

3. Geometry Formulas in Quadrilaterals:

1. Area of a trapezium with a pair of sides parallel to each other is

½ × (sum of the parallel sides) × (distance between the parallel sides)

2. Area of a parallelogram with base ‘b’ and height ‘h’ is b × h

3. Area of a rhombus is

½ × (product of length of diagonals)

4. Area of a rectangle is l × b, where l is length and b is breadth of the rectangle.

5. Area of a square with all sides of length ‘a’ is a2. If d is length of a diagonal of the square, then its area is ½ d2

4. Geometry Formulas in Three dimensional figures:

1. Consider a cube in which all sides are equal in length. Say, it is a. Then,

Total surface area of the cube is 6a2. Volume of the cube is a3

2. Consider a cuboid with sides whose lengths are l, b and h. Then,

Total surface area of the cuboid is 2lh + 2lb + 2bh. Volume of the cuboid is l × b × h

3. Consider a right circular cylinder having radius ‘r’ and height h. Then,

Total surface area of the cylinder is 2Πrh + 2Πr2. Volume of the cylinder is Πr2h

4. Consider a right circular cone having radius ‘r’ , vertical height ‘h’ and slant height ‘l’. Then,

Total surface area of the cone is Πrl + Πr2. Volume of the cone is (1/3) × Πr2h

5. Consider a sphere of radius ‘r’. Then,

Total surface area of the sphere is 4Πr2. Volume of the sphere is (4/3) Πr3

6. Consider a hemi-sphere of radius ‘r’. Then,

Total surface area of the hemi-sphere is 3Πr2. Volume of the hemi-sphere is (2/3) Πr3