If the length of two diagonals of a rhombus are 6 cm and 4 cm, then its area is :

1. 10 cm²

2. 12 cm²

3. 14 cm²

4. 16 cm²

Case Study:
In most of the Indian metropolitan cities, government has made many flyovers to regulate the traffic flow. One of such flyover is shown below. The triangular side walls of the flyover have been used for advertisements. One of such side walls has lengths 122 m, 120 m and 22 m. The rate of advertisement on this wall is ₹ 1,000 per m² per year. A private company hired this wall for 4 months.

Based on the above information, answer the following questions:

1. Semi-perimeter of the triangular wall is :
   (a) 130 m
   (b) 132 m
   (c) 134 m
   (d) 135 m

2. Area of the triangular wall is :
   (a) 1400 m²
   (b) 1350 m²
   (c) 1340 m²
   (d) 1320 m²

3. Total amount paid by the company as rent for the wall is:
   (a) ₹4,00,000
   (b) ₹4,20,000
   (c) ₹4,40,000
   (d) ₹13,20,000

4. Another company paid ₹5,50,000 as a rent for the same wall. For how many months did the company hire the wall?
   (a) 5
   (b) 6
   (c) 7
   (d) 8

5. Which of the following is the correct formula for finding the area of a triangle of sides x, y, z and semi perimeter p?
   (a) Area = p(p - x) (p - y) (p - z)
   (b) Area = $\sqrt{p(p + x)(p + y)(p + z)}$
   (c) Area = $\sqrt{(p - x)(p - y)(p - z)}$
   (d) Area = $\sqrt{p(p - x)(p - y)(p - z)}$

Assertion (A): An isosceles right triangle has area 8 cm². The length of its hypotenuse is 4 cm.

Reason (R): Area of an isosceles triangle with sides a, a and b is given by $\dfrac{1}{4}b\sqrt{4a^2 + b^2}$.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Assertion (A): The area of rhombus is 84 cm². If its one diagonal is 7 cm, then side of the rhombus is 12 cm.

Reason (R): Area of rhombus is given by $\dfrac{1}{2}$ × product of its diagonals.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false