Question

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Answer 1

Volume = 2880m²

Surface area = 1632m²

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

`A=(bh)/(2)`

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

`A=(12*16)/(2) \\12*16=192\\(192)/(2) =96`

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 =
`SA=bh+L(s_1+s_2+s_3)`

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

`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`

So we can conclude that the surface area of the triangular prism is 1632m²