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 (Diagonal) ^{2} = (Length) ^{2} + (Breadth) ^{2} (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 d_{1} and d_{2} 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 = (ab), i.e., the difference between the parallel sides and c and d are the two nonparallel sides of the trapezium. Also,
(C) Circles(i) Circumference of a circle = 2πr (ii) Area of Circle = πr^{2} (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 (ii) When the path is within the garden, surrounded by it (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 twodimensional figure is changed by x%, its area changes by . 7. If all the measuring sides of any twodimensional 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 cm^{2}, 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 2r^{2}. 11. The area of the largest triangle inscribed in a semicircle of radius r is r^{2}. Area Aptitude Test Paper 1 Area Aptitude Test Paper 2 Area Aptitude Test Paper 3 Area Aptitude Test Paper 4 Area Aptitude Test Paper 5 Area Aptitude Test Paper 6 Area Aptitude Test Paper 7 Area Aptitude Test Paper 8
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