Area Aptitude Concepts and Formulas

(A) Triangle:

(i) Area of triangle = 

 × Base × height

(ii) If a, b, c are the lengths of the sides of a triangles and s =  (a+b+c):

(iv) Area of equilateral triangle=  ×(side)²

Perimeter of an equilateral triangle = 3 × side

(B) Quadrilaterals:

(i) Area of a rectangle = Length x Breadth
Length of rectangle =  Breadth of rectangle= 

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

(ii) Area of Parallelogram:

If a, b, c, and d are the lengths of a parallelogram,

(iii) Area of a square: (side)² = (diagonal)²

Perimeter of a square = 4 x side

Area of Rhombus = × (Product of diagonals)

When d₁ and d₂ are the two diagonals, then the side of rhombus = 

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

(vi) Area of Parallelogram = (Base x Height).

(vii) Area of trapezium =  (sum of parallel sides perpendicular distance between them)

=  (a+b)h

Where a, and b are the parallel sides of the trapezium and h is the perpendicular distance between the sides ‘a’ and ‘b’.

Where k = (a-b), i.e., the difference between the parallel sides and c and d are the two non-parallel sides of the trapezium. Also,

(C) Circles

(i) Circumference of a circle = 2πr

(ii) Area of Circle = πr²

(iii) Arc AB = , where ∠AOB= θ and O is the center.

(iv) Area of sector AOB = 

(v) Area of Sector AOB = × arc AB × r

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Some Quicker Methods:

1. Carpeting a Floor:

(i) Length of the carpet required = 

(ii) Amount Required = Rate per meter ×

2. Paving with tiles:

(i) Number of tiles required = 

(ii) The side of the largest possible square tile = HCF of length and breadth of the room.

3. Path around a garden, verandah around a room.

(i) When verandah is outside the room, surrounding it
Area of verandah = 2 (width of verandah) x [length + breadth of room + 2(width of verandah)].

(ii) When the path is within the garden, surrounded by it
Area of path = 2(width of path) x [length + breadth of garden – 2(width of path)].

(iii) When the area of the path is given, to find the area of the garden enclosed (the garden is square in shape).

Area of square garden = 

4. Rhombus

(i) Area of a rhombus = 1/2 * (product of diagonals)

5. If the length and breadth of a rectangle is increased by x and y percent respectively, the area is increased by.

6. If all the measuring sides of any two-dimensional figure is changed by x%, its area changes by .

7. If all the measuring sides of any two-dimensional figure are changed (increased or decreased) by x%, its perimeter also changes by x%.

8. If all the sides of a quadrilateral are increased by x%, its corresponding diagonals also increased by x%.

9. If the area of a square is x cm², the area of the circle formed by the same perimeter is given by .

10. Area of a square inscribed in a circle of radius r is 2r².

11. The area of the largest triangle inscribed in a semi-circle of radius r is r².

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