Question

Find the lateral area and the surface area of the right prism.

Answer 1

Answer:

390 $in^{2}$

Step-by-step explanation:

We know that the top is a rectangle triangle, we only have two of the tree sides and the one that is missing is the hypotenuse. The formula to find it is $h^{2}= a^{2} +b^{2}$

If we put the values we know it would be

$h^{2}= 5^{2} +12^{2}$

$h^{2}= 25 +144$

$h^{2}= 169$

$h=\sqrt{169}$ = 13

So now we have the lenght missing.

The area of the top and bottom is the same and we found it by the formula $\frac{(base)(height)}{2}$ = $\frac{(12)(5)}{2}$ = 30, that is the area of just one triangle, multiply by 2 and that is the area of top and bottom = 30 x 2 = 60

The area of a rectangle is base x height, we have three rectangles.

First one: 13 x 11 = 143

Second one: 5 x 11 = 55

Third one: 12 x 11 = 132

The sum of the areas would be = 60 + 143 + 55 + 132 = 390 $in^{2}$