# Important Questions for Chapter 12 - Heron's Formula

The provided PDF is a complete set of important questions for CBSE class 9th Maths prepared by our subject experts contains all the explanations and step by step solutions for the chapters and topics in Maths. Practice these questions and score more i your tests and examination.

**Important questions based on NCERT syllabus for Chapter 12 - Heron's Formula:**

*Question 1*: A triangular advertisement board has sides 11m,15m and 6m. If the advertisement yields an earning of Rs. 1000/ m^2 per month. So how much the company will earn in 3 and half years?

*Solution*:

Semi perimeter of a triangle = (a+b+c)/2

⇒ (11+15+6)/2 = 16cm

Area of a triangle = √(s(s-a)(s-b)(s-c))

= √(16(16-11)(16-15)(16-6))

= √800

= 20 √2 cm^2

If the advertisement yields an earning of Rs. 1000 /m^2 per month,

Then the earning in 42 months = 20√2 × 1000 × 42 = Rs. 840000√2

*Question 2*: Find the area of a quadrilateral ABCD in which AB = 6 cm, BC = 8 cm, CD = 8 cm, DA = 10 cm and AC = 10 cm.

*Solution*:

Take ΔABC

S = Perimeter/2 = (10+8+6)/2 = 12cm

Area = √(s(s-a)(s-b)(s-c))

= √(12(12-10)(12-8)(12-6))

= √576

= 24 cm^2

Now take ΔCDA

S = Perimeter/2 = (10+8+10)/2 = 14cm

Area = √(s(s-a)(s-b)(s-c) )

= √(14(14-10)(14-8)(14-10))

= √1344 = 6.66 cm^2

Area of Quadrilateral = 24 + 36.66 = 60.66 cm^2

*Question 3*: A wall is in the shape of a trapezium whose parallel sides are 50 m and 20 m. The non-parallel sides are 28 m and 26 m. Find the area of the wall.

*Solution*:

Draw a line CE parallel to AD and draw a perpendicular CF on AB.

It can be observed that AECD is a parallelogram.

CE = AD = 26 m

AE = DC = 50 m

BE = 50 − AB = 50m - 20 m = 30m

For ΔBEC,

s = Perimeter/2 = (26+28+30)/2 = 42cm

Area of the ΔBEC = √(s(s-a)(s-b)(s-c))

= √(42(42-26)(42-28)(42-30))

= 336 cm^2

Now, area of ΔBEC = 1/2 × base × height

= 1/2 × BE × CF

= 1/2 × 30 × CF

CF = 672/30

= 22.4cm

Area of AECD = CF × AE

= 22.4 × 50

= 1120 cm^2

Therefore, the area of wall = 1120 - 336 = 784 cm^2.