Question

What is the total surface area of the triangular prism? DO NOT PUT LABEL ON ANSWER.

Answer 1

We need to find the total surface area of the triangular prism. We have two triangles at the bases, and three rectangular at the lateral area. Then, we can find the area for one of the triangles (because the other is congruent), and we also need to find the area of one of the rectangles. Then, we will need to multiply the areas by two (in the case of the triangles), and we need to find the areas for each rectangle (they are not congruent). Then, we have:

Area of the triangle:

We have here a right triangle, and its height and base are:

b = 6 ft.

h = 8 ft.

And we know that the area of a triangle is given by:

`A_{\text{triangle}}=(b\cdot h)/(2)=(6\cdot8)/(2)=(48)/(2)\Rightarrow A_(triangle)=24ft^2`

Area of the rectangle 1:

We have that one rectangle has one side is equal to 10 ft, and the other of 7.5 ft. Then, we know that the area of a rectangle is:

`A_{\text{rectangle}1}=l\cdot h`

Then, we have:

`A_{\text{rectangle}1}=10\cdot7.5=75ft^2\Rightarrow A_(rec\tan gle)=75ft^2`

Area of the rectangle 2:

We can use the same procedure as before:

`A_{\text{rectangle}2}=l\cdot h=7.5\cdot8=60ft^2`

Area of the rectangle 3:

`A_{\text{rectangle}3}=l\cdot h=6\cdot7.5=45ft^2`

Now, the total surface area of the triangular prism is (we explained this above):

2 * Area of triangle + Area of rectangle 1 + Area of rectangle 2 + Area of rectangle 3

Thus, we have:

`2\cdot24ft^2+75ft^2+60ft^2+45ft^2=48ft^2+180ft^2=228ft^2`

Therefore, the total surface area of the triangular prism is equal to 228 sq. ft.