Answer:
Volume = 2880m²
Surface area = 1632m²
Step-by-step explanation:
The prism shown is a triangular prism
The volume of the prism can be found by multiplying the area of the base by the length of the prism
The base being a triangle.
The area of a triangle can be calculated by using this formula
[tex]A=\frac{bh}{2}[/tex]
where b = base length and h = height
The base length of the particular triangle is 12 m and the height is 16
That being said we plug in the values into the formula
[tex]A=\frac{12*16}{2} \\12*16=192\\\frac{192}{2} =96[/tex]
Hence the area of the base is 96 square meters
Finally we multiply the area of the base by the length of the prism ( which is 30 m )
So volume = 96 * 30
96 * 30 = 2880
Hence the volume of the triangular prism is 2880m²
Now to find the surface area
Kindly check the image below for information on the formula for surface area of a triangular prism
Formula = [tex]SA=bh+L(s_1+s_2+s_3)[/tex]
where b = base length
h = height of base
L = length of prism
S1 also = base
S2 = base height
S3 = slant height of base
The shown triangle has the following dimensions
b = 12
h = 16
L = 30
S1 = 12
S2 = 16
S3 = 20
Now that we have identified each dimension, we plug in the values into the formula
[tex]SA=16*12 + 30(12+16+20)\\16*12=192\\30*12=360\\30*16=480\\30*20=600\\600+192+480+360=1632\\SA=1632m^2[/tex]
So we can conclude that the surface area of the triangular prism is 1632m²
