Question

three sides of a triangle ,find area by using heron's formula
(1)  a =20 cm,b=30 cm,c=50 cm
(2)   a=24 cm ,b=26 cm,c=20 cm
(3)   a=b=c=36 cm
(4)a=b=18 cm ,c=24 cm

Answer 1

1 )
p=a+b+c/2
p=(20+30+50)/2
p=100/2
p=50  where p= semiperimeter

area=$\sqrt{p(p-a)(p-b)(p-c)}$
area= rad 50*(50-20)(50-30)(50-50)
area= rad 50*30*50*0
area= rad 0
area=0

2) p=24+26+20/2
p=70/2
p=35

area= rad 35*(35-24)(35-26)(35-20)
area= rad 35*11*9*15
area= rad 51975
area= rad 3^3*5^2*7*11
area= rad 3^2*3*5^2*7*11
area=5*3 rad 3*7*11
area=15 rad 231

3)  a=b=c=36
p=36+36+36/2
p=108/2
p=54

Area= rad 54 (54-36)(54-36)(54-36)
area=rad 54*18*18*18
area= rad 2*3^3 * 2*3^2 * 2*3^2 * 2*3^2
area= rad 2^4*3^9
area=4*81 rad 3
area=324 rad 3

4) a=b=18 cm ,c=24 cm
p=18+18+24/2
p=30

area= rad 30 (30-18)(30-18)(30-24)
area= rad 30*12*12*6
area= rad 25920
area= rad 2^6*3^4*5
area= 72 rad 5