Respuesta :
Answer:
The surface Area of the prism is 540 square centimeters.
Step-by-step explanation:
Given:
Base side [tex]a[/tex] = 5 cm
Base side [tex]b[/tex] = 13 cm
Base side [tex]c[/tex] = 12 cm
Height of the prism [tex]h[/tex] = 16 cm
We need to find the surface area of the prism.
Solution:
Now we know that;
Given prism is a right angled triangular prism.
The formula for Surface area of triangular prism is given by;
[tex]A=2A_B+(a+b+c)h[/tex]
where [tex]A_B[/tex] ⇒ Lateral Surface area.
[tex]A_B=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s=\frac{a+b+c}{2}[/tex]
First we will find the value of 's'.
[tex]s= \frac{a+b+c}{2} =\frac{5+12+13}{2}=\frac{30}{2}=15[/tex]
Now we will find [tex]A_B[/tex]
[tex]A_B=\sqrt{s(s-a)(s-b)(s-c)}\\\\A_B= \sqrt{15(15-5)(15-13)(15-12)}\\\\A_B= \sqrt{15\times 10\times2\times3}\\\\A_B=\sqrt{900}\\ \\A_B=30\ cm^2[/tex]
Now we will find the surface area of the prism [tex]A[/tex]
[tex]A=2A_B+(a+b+c)h[/tex]
[tex]A = 2\times 30+(5+13+12)16\\\\A=60+30\times 16\\\\A=60+480\\\\A=540\ cm^2[/tex]
Hence The surface Area of the prism is 540 square centimeters.
