Question

utilizando a formula de harão calcule a area de um triangulo cujos lados medem:

Answer 1

Explicação passo-a-passo:

a)

$\sf p=\dfrac{5+7+4}{2}$

$\sf p=\dfrac{16}{2}$

$\sf p=8$

$\sf S=\sqrt{p\cdot(p-a)\cdot(p-b)\cdot(p-c)}$

$\sf S=\sqrt{(8\cdot(8-5)\cdot(8-7)\cdot(8-4)}$

$\sf S=\sqrt{8\cdot3\cdot1\cdot4}$

$\sf S=\sqrt{96}$

$\sf S=4\sqrt{6}~m^2$

b)

$\sf p=\dfrac{12+15+9}{2}$

$\sf p=\dfrac{36}{2}$

$\sf p=18$

$\sf S=\sqrt{p\cdot(p-a)\cdot(p-b)\cdot(p-c)}$

$\sf S=\sqrt{(18\cdot(18-12)\cdot(18-15)\cdot(18-9)}$

$\sf S=\sqrt{18\cdot6\cdot3\cdot9}$

$\sf S=\sqrt{2916}$

$\sf S=54~dm^2$

c)

$\sf p=\dfrac{2+3+4}{2}$

$\sf p=\dfrac{9}{2}$

$\sf p=4,5$

$\sf S=\sqrt{p\cdot(p-a)\cdot(p-b)\cdot(p-c)}$

$\sf S=\sqrt{(4,5\cdot(4,5-2)\cdot(4,5-3)\cdot(4,5-4)}$

$\sf S=\sqrt{4,5\cdot2,5\cdot1,5\cdot0,5}$

$\sf S=\sqrt{8,4375}$

$\sf S=\sqrt{\dfrac{84375}{10000}}$

$\sf S=\dfrac{75\sqrt{15}}{100}$

$\sf S=\dfrac{3\sqrt{15}}{4}~km^2$

d)

$\sf p=\dfrac{14+16+10}{2}$

$\sf p=\dfrac{40}{2}$

$\sf p=20$

$\sf S=\sqrt{p\cdot(p-a)\cdot(p-b)\cdot(p-c)}$

$\sf S=\sqrt{(20\cdot(20-14)\cdot(20-16)\cdot(20-10)}$

$\sf S=\sqrt{20\cdot6\cdot4\cdot10}$

$\sf S=\sqrt{4800}$

$\sf S=40\sqrt{3}~cm^2$