# Area Formulas

### FUNDAMENTAL CONCEPTS

*1. Results on Triangles:*

- Sum of the angles of a triangle is 180°.
- The sum of any two sides of a triangle is greater than the third side.
In a right-angled triangle, (Hypotenuse)**Pythagoras Theorem**:^{2}= (Base)^{2}+ (Height)^{2}.- The line joining the mid-point of a side of a triangle to the positive vertex is called the
.*median* - The point where the three medians of a triangle meet, is called
*centroid.*The centroid divided each of the medians in the ratio 2 : 1. - In an isosceles triangle, the altitude from the vertex bisects the base.
- The median of a triangle divides it into two triangles of the same area.
- The area of the triangle formed by joining the mid-points of the sides of a given triangle is one-fourth of the area of the given triangle.

*2. Results on Quadrilaterals:*

- The diagonals of a parallelogram bisect each other.
- Each diagonal of a parallelogram divides it into triangles of the same area.
- The diagonals of a rectangle are equal and bisect each other.
- The diagonals of a square are equal and bisect each other at right angles.
- The diagonals of a rhombus are unequal and bisect each other at right angles.
- A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
- Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.

### IMPORTANT FORMULAE

**I.** 1. Area of a rectangle = (Length x Breadth).

Length = and Breadth =

2. Perimeter of a rectangle = 2(Length + Breadth).

**II.** Area of a square = (side)^{2} = (diagonal)^{2}.

**III.** Area of 4 walls of a room = 2 (Length + Breadth) x Height.

**IV. **1. Area of a triangle = x Base x Height.

2. Area of a triangle =

where *a*, *b*, *c* are the sides of the triangle and *s* = (*a* + *b* + *c*).

3. Area of an equilateral triangle = x(side)²

4. Radius of in circle of an equilateral triangle of side *a* =

5. Radius of circumcircle of an equilateral triangle of side *a* =

6. Radius of incircle of a triangle of area and semi-perimeter *s* =

**V**. 1. Area of parallelogram = (Base x Height).

2. Area of a rhombus = x (Product of diagonals).

3. Area of a trapezium = x (sum of parallel sides) x distance between them.

**VI.** 1. Area of a circle = R² , where R is the radius.

2. Circumference of a circle = 2R.

3. Length of an arc = where is the central angle.

4. Area of a sector = (arc x R)=

**VII.** 1. Circumference of a semi-circle = R.

2. Area of semi-circle =