In this page, we will discuss special formulas and methods for:

How to calculate area of:

- A triangle, when the length of its three sides are given
- A square, when the length of its diagonal is given
- A rectangle, the lengths of whose diagonal and perimeter are given

Question:

How to calculate area of a triangle if the lengths of its three sides are given?

Answer:

Use heron’s formula to calculate area of a triangle when the lengths of its three sides are given.

And, Heron’s formula is

In the formula, **a, b and c** denote the lengths of the three sides of the triangle; and **s** is the semi-perimeter of the triangle, i.e.

**s = (a+ b + c)/2**

For example, the area of a triangle in which the lengths of the three sides are 6, 8 and 10 is

**How to calculate area of a square when its diagonal length is given? **

To calculate area of a square using its diagonal, the formula is

The area of a square whose diagonal length is 10 cms is

10^{2}/2 = 100/2 = 50 sq. cms.

**How to calculate area of a rectangle whose perimeter and diagonal lengths are given? **

In a rectangle, if length is **l** and breadth is **b**, then

Perimeter of the rectangle = 2 (l + b) and

Diagonal length = √(l^{2} + b^{2})

Apply the algebraic identity below, to calculate area of the rectangle:

(l + b)^{2} = l^{2} + b^{2} + 2lb,

Transpose l^{2} + b^{2} to the other side, so

2lb = (l + b)^{2} – ( l^{2} + b^{2}),

Next divide by 2 to finally calculate area of the rectangle as below:

l× b = ((l + b)^{2} – (l^{2} + b^{2}))/2

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