Area Aptitude Concepts and Formulas
(i) Area of triangle =
(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
(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)
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,
(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
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 =
(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.
Area Aptitude Test Paper 2
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Area Aptitude Test Paper 7