Answer:
205.9 cubic feet
Step-by-step explanation:
To find the volume of the triangular prism, we'll first calculate the area of the triangular base and then multiply it by the height of the prism.
Given that the base of the triangular prism has sides measuring 3 ft, 3 ft, and 22 ft, the area of the triangular base can be calculated using Heron's formula:
Heron's formula states that for a triangle with side lengths
�
a,
�
b, and
�
c, and semi-perimeter
�
s:
Area
=
�
(
�
−
�
)
(
�
−
�
)
(
�
−
�
)
Area=
s(s−a)(s−b)(s−c)
where
�
s is the semi-perimeter of the triangle, given by:
�
=
�
+
�
+
�
2
s=
2
a+b+c
In this case,
�
=
3
a=3 ft,
�
=
3
b=3 ft, and
�
=
22
c=22 ft. We'll first calculate the semi-perimeter
�
s:
�
=
3
+
3
+
22
2
=
28
2
=
14
s=
2
3+3+22
=
2
28
=14
Now, we can calculate the area of the triangular base using Heron's formula:
Area
=
14
(
14
−
3
)
(
14
−
3
)
(
14
−
22
)
Area=
14(14−3)(14−3)(14−22)
Area
=
14
×
11
×
11
×
(
−
8
)
Area=
14×11×11×(−8)
Area
=
1694
Area=
1694
Area
≈
41.18
square feet
Area≈41.18 square feet
Now that we have the area of the triangular base, we'll multiply it by the height of the prism, which is 5 ft:
Volume
=
Area of base
×
Height
Volume=Area of base×Height
Volume
=
41.18
×
5
Volume=41.18×5
Volume
=
205.9
cubic feet
Volume=205.9 cubic feet
Therefore, the volume of the triangular prism is approximately
205.9
205.9 cubic feet.
