Question

Find the Surface Area of the triangular Prism below:

Answer 1

≈ 12,78 m^2

Explanation:

The surface area is equal to the sum of the areas of all the sides

This figure has sides of 2 triangles (bases) and 3 rectangles (lateral surface)

h (triangle) = 1m

We can find the base of the triangle by using the Pythagorean theorem (multiply by 2, because the triangle's base contains two of these identicals sides)

`(( {1.5})^(2) - {1}^(2) ) * 2=( 2.25 - 1 ) * 2= 1.25 * 2 = 2.5> 0`

The triangle's base is equal to:

`√(2.5) = ( √(10) )/(2)`

First, let's find the area of 2 bases (triangles):

`a(bases) = 2 * (1)/(2) * 1 * ( √(10) )/(2) = ( √(10) )/(2)`

Now, we can find the whole surface area by adding the areas of the rectangles to the bases' areas:

`a(surface) = ( √(10) )/(2) + 2.4 * 2 + 1.5 * 2 + 1.7 * 2 = ( √(10) )/(2) + (56)/(5) ≈12.78`