Question

calcule a area de cada triangulo

Answer 1

Explicação passo-a-passo:

a)

$\sf p=\dfrac{16+18+20}{2}$

$\sf p=\dfrac{54}{2}$

$\sf p=27$

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

$\sf S=\sqrt{27\cdot(27-16)\cdot(27-18)\cdot(27-20)}$

$\sf S=\sqrt{27\cdot11\cdot9\cdot7}$

$\sf S=\sqrt{18711}$

$\sf S=9\sqrt{231}~dm^2$

b)

$\sf S=\dfrac{b\cdot h}{2}$

$\sf S=\dfrac{12\cdot16}{2}$

$\sf S=\dfrac{192}{2}$

$\sf S=96~dm^2$

c)

Pelo Teorema de Pitágoras:

$\sf (b_1)^2+12^2=20^2$

$\sf (b_1)^2+144=400$

$\sf (b_1)^2=400-144$

$\sf (b_1)^2=256$

$\sf b_1=\sqrt{256}$

$\sf b_1=16~dm$

$\sf (b_2)^2+12^2=15^2$

$\sf (b_2)^2+144=225$

$\sf (b_2)^2=225-144$

$\sf (b_2)^2=81$

$\sf b_2=\sqrt{81}$

$\sf b_2=9~dm$

O outro lado desse triângulo mede:

$\sf b=b_1+b_2$

$\sf b=16+9$

$\sf b=25~dm$

Logo:

$\sf S=\dfrac{b\cdot h}{2}$

$\sf S=\dfrac{25\cdot12}{2}$

$\sf S=\dfrac{300}{2}$

$\sf S=150~dm^2$

Answer 2

Resposta:

Explicação passo-a-passo:

p= (a  +b  +  c ) /2

p= (18 + 20 + 16)/2

p= 54/2

p=27 dm

A= $\sqrt{p*(p-a)*(p-b)*(p-c)}$

A= √27*(27-18)*(27-20)*(27-16)

A= √27*9*7*11

A = √18711

A= 9√241

b)    A= b*h/2

A= 12*16/2

A= 192/2

A= 96 dm²

c) a²=b²+c²

15²=12²+c²

225-144=c²

c²= 81

c=√81

c= 9

a²= b²+c²

20²=12²+c²

400= 144+c²

c²= 400-144

c²=256

c=√256

c= 16

A= b*h/2

A= 25*12/2

A=300/2

A= 150 d m²