Solve for the surface area

Question

Find the surface area

https://ibb.co/d0fLyYnF

Answer 1

Hi Sjs E.

Question does your diagram contain Two Congruent Triangles and Three Rectangles is it the Net for a Triangular Prism?

If yes, then calculate the value of the missing side for the Right Triangle this will confirm whether or not the given height is a perpendicular bisector to the base of the triangle, then use the appropriate area formula for shapes in the net. Add the surface areas together to get the total for the figure.

I hope this helps.

Answer 2

In a triangular prism, the two triangular faces will have equal side and height measures. You were given the height of one of these triangles--8, which means you know the height of the other right triangle.

Formula for area of a right triangle is:

A = (1/2)bh

h= 8

For the base: you were given 12 for the length of the total triangle; right angle bisects that, which means it divides into two--base = 6. You could also use the Pythagorean Theorem since you were given a hypotenuse of 10--10^2 = 8 ^2 + b^2; b^2= 36, b = 6

A = (1/2)(8)(6) = 24

But that's only one right triangle out of four--the two triangle faces are composed of two right triangles each. So multiply that area by 4 to get the total area of your triangles:

4A = 4(24) = 96

Now, the rectangles are easier to work with:

A=lw; l = 15.5, w = 10

A = 155

But you have two of these, so multiply:

2A = 2(155) = 310

Now, we have one more face to deal with: the base, also a rectangle, but with different width:

A=lw

l = 15.5, w = 12

A= (15.5*12) = 186

Add up everything in bold:

SA = 96 + 310 + 186 = 592

I hope this helps.