PRACTICE PROBLEMS USING HERONS FORMULA 

Question 1 :

The perimeter of a triangular plot is 600 m. If the sides are in the ratio 5 : 12 : 13, then find the area of the plot.

Solution :

The sides of triangle be 5x, 12x and 13x.

Perimeter of triangular plot  =  600

5x + 12x + 13x  =  600

30x  =  600

x  =  600/30  =  20

5x  =  5(20)  =  100

12x  =  12(20)  =  240

13x  =  13(20)  =  260

s  =  600/2  =  300

s - a  =  300 - 100  =  200

s - b  =  300 - 240  =  60

s - c  =  300 - 260  =  40

 √s(s − a)(s − b)(s − c)   =   √300(200)(60)(40) 

=   √(3 ⋅ 10 ⋅ 10 ⋅ 2 ⋅ 10 ⋅ 10 ⋅ 3 ⋅ 2 ⋅ 10 ⋅ 2 ⋅ 2 ⋅10)

   =  12000 m²

Question 2 :

Find the area of an equilateral triangle whose perimeter is 180 cm.

Solution :

Perimeter of equilateral triangle  =  180 cm

3a  =  180

a  =  180/3  =  60 cm

Area of equilateral triangle = (√3/4)a²

=  (√3/4)60²

=  900√3

=  900(1.732)

=  1558.8 cm²

Question 3 :

An advertisement board is in the form of an isosceles triangle with perimeter 36 m and each of the equal sides are 13 m. Find the cost of painting it at ₹ 17.50 per square metre.

Solution :

Let "x" be the unknown side of the triangle.

Then sides of triangle are x, 13 and 13.

perimeter   =  36 m

x + 13 + 13  =  36

x + 26  =  36

x  =  36 - 26  =  10 m

a = 10, b = 13 and c = 13

height  =  √13² - 5²

  =   √(169 - 25)

  =   √144

height   =  12 cm

Area of triangle  =  (1/2) x base x height

=  (1/2) x 10 x 12

  =  60 cm²

Cost of of painting it at ₹ 17.50 per square metre

 Required cost  =  60 (17.50)

  = ₹ 1050

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.