Question

Find the area using heron's formula: (1) 60, 50, 100 (2) 8, 8,10

Answer 1

Answer:

1) 1140 sq. unit      2) 31.224 sq. units

Step-by-step explanation:

1) a = 60

  b = 50

  c = 100

semi perimeter s = a+b+c / 2

                            = 210 / 2

                            = 105

Heons Formula =  $\sqrt{s(s-a)(s-b)(s-c)}$        

Area of triangle = sqrt [(105) x (105-60) x (105-50)(105-100) ]

                          = sqrt [105 x 45 x 55 x 5]

                          = sqrt [1299375]

                          = 1140 unit sq.

2) a = 8

   b = 8

   c = 10

semi perimeter s = a+b+c / 2

                            = 26 / 2

                            = 13

Using Herons formula = $\sqrt{s(s-a)(s-b)(s-c)}$

                           Area = sqrt [ (13) (13-8) (13-8) (13-10)]

                                    = sqrt [ 13 x 5 x 5 x 3 ]

                                    = sqrt [975]

                                    = 31.224 unit sq.

       

Answer 2

Answer:

heron's formula =

s = a+b+c/2

area = √s(s-a)(s-b)(s-c)

1. s = 60+50+100/2

s = 210/2 = 105

area = √105(105-60)(105-50)(105-100)

= 75√231 ~ 1139.90 .sq unit

2. s = 8+8+10/2

s = 26/2 = 13

area = √13(13-8)(13-8)(13-10)

= 5√39 ~ 31.224 .sq unit