a = 8cm
b = 6cm
c = 13cm
Ze wzoru Herona:
P = √p(p-a)(p-b)(p-c) gdzie p = 0,5(a+b+c)
p = 0,5(8cm + 6cm + 13cm) = 13,5cm
p-a = 13,5cm-8cm = 5,5cm
p-b = 13,5cm-6cm = 7,5cm
p-c = 13,5cm-13cm = 0,5cm
P = √13,5cm*5,5cm*7,5cm*0,5cm = 16,69cm²
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Stosujemy tu wzór Herona:
P = √[p(p - a)(p - b)(p - c)]
a = 8cm b = 6cm c = 13cm
p = 1/2*(a +b + c) = 1/2 * (8 + 6 + 13) = 1/2 * 27 = 13,5
P = √[13,5(13,5 - 8)(13,5 - 6)(13,5 - 13)]
P = √[13,5 * 5,5 * 7,5 * 0,5)
P = √278,4375
P = 16,6864... ~ 16,69cm²