What is surface area ?
The surface area of a solid object is defined as the area that the object occupies. To find the surface area we must find the total area of its faces.
Here, we are given a triangular prism and we are asked to find its surface area.
How do we find the surface area of a triangular prism?
We can find the area of a triangular prism using the following formula (as shown in the attached image, Please note that "b" and "s2" have the same defined length) :
(S + b + h)L + bh
Where
- S = Slant length
- b = the length of the base
- H = height of triangle
- L = length of prism
Here, we are given the length of the base(8in), the height(15in) and the length of the prism(21in); however we are not given the slant length. so we must find it.
Finding the slant length
If we ignore the prism itself and look at the base, we notice that the base is a right angled triangle. Within the triangle we have its base length and height and we need to find the hypotenuse. We can do so by using the Pythagorean theorem: a² + b² = c² where a and b = length of legs and c = hypotenuse.
Here a and b = 15 and 8.
By plugging in these values we acquire:
==> 15² + 8² = c²
==> 225 + 64 = c²
==> 289 = c²
==> 17 = c
So the hypotenuse (or slant length) = 17
Finding the surface area
Now that we have identified all the variables we can finally plug in the values to get the surface area.
We have
Plugging this into (S + b + h)L + bh, we acquire
==> (17 + 8 + 15)21 + 8(15)
==> 40(21) + 8(15)
==> 840 + 8(15)
==> 840 + 120
==> 960
The surface area is 960 in²