Question

Find the surface area of the prism. A drawing of a right triangular prism. The triangular faces have perpendicular sides 5 centimeters and 12 centimeters and the third side is 13 centimeters. The height of the prism is 16 centimeters.

Answer 1

Answer:

The surface Area of the prism is 540 square centimeters.

Step-by-step explanation:

Given:

Base side $a$ = 5 cm

Base side $b$ = 13 cm

Base side $c$ = 12 cm

Height of the prism $h$ = 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;

$A=2A_B+(a+b+c)h$

where $A_B$ ⇒ Lateral Surface area.

$A_B=\sqrt{s(s-a)(s-b)(s-c)}$

$s=\frac{a+b+c}{2}$

First we will find the value of 's'.

$s= \frac{a+b+c}{2} =\frac{5+12+13}{2}=\frac{30}{2}=15$

Now we will find $A_B$

$A_B=\sqrt{s(s-a)(s-b)(s-c)}\\\\A_B= \sqrt{15(15-5)(15-13)(15-12)}\\\\A_B= \sqrt{15\times 10\times2\times3}\\\\A_B=\sqrt{900}\\ \\A_B=30\ cm^2$

Now we will find the surface area of the prism $A$

$A=2A_B+(a+b+c)h$

$A = 2\times 30+(5+13+12)16\\\\A=60+30\times 16\\\\A=60+480\\\\A=540\ cm^2$

Hence The surface Area of the prism is 540 square centimeters.