a glass prism used in the study of optics has a right triangular base. Th legs of the triangle are 3.00cm and 4.00cm. The prism is 8.50cm high. what is the total surface area of the prism?

Question

anonymous · Answer

i did 4*8.5+3*8.5+12*8.5=102 is this correct? and what to do next?

anonymous · Answer

The prism has 5 sides, we must find the area of each one. 2 of the sides will be called the "ends" that you can see in the image. They are calculated simply by the equation of a triangle:

A=(1/2)*b*h

A=(1/2)*4*3=6 cm squared

We multiply this value by 2 because there are two "ends" to the prism

so Aends= 2*6= 12 cm squared

Now we must find the area of the rectangular pieces of the prism:

A1=3*8.5=22.5 cm squared

A2=4*8.5=34 cm sqared

The last side must use the Pythagorean theorem to find the length:

$$\sqrt{3^{2}+4^{2}}=5$$

A3=8.5*5= 42.5 cm squared




Adding all the areas gives you:

Aends +A1 +A2 +A3=   111 cm squared

anonymous · Answer

thanks for explaining