Alex made a sketch for a homemade soccer goal he plans to build. The goal will be in the shape of a triangular prism. The legs of the right triangles at the sides of his goal measure 4 ft and 8 ft, and the opening along the front is 24 ft. How much space is contained within the goal?
area of triangle times the length.
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Explanation: V= B*h
B= 1/2( 4*8)= 1/2(32)= 16 inches ^ 2
Height of the prism= 24 inches
V= B*h= v= 24*16= V= 384 feet ^ 3
Answer= 384 feet ^ 3
To find the space contained within the goal, we need to calculate the volume of the triangular prism.
The volume of a triangular prism is given by the formula:
Volume = Base Area x Height
In this case, the base of the triangular prism is a right triangle, and the height is the length of the opening.
Let's label the legs of the right triangle as A = 4 ft and B = 8 ft.
To find the length of the hypotenuse, C, we can use the Pythagorean theorem:
C^2 = A^2 + B^2
Plugging in the values, we have:
C^2 = 4^2 + 8^2
C^2 = 16 + 64
C^2 = 80
C = √80
C ≈ 8.94 ft (rounded to two decimal places)
Now that we know the dimensions of the base, we can calculate the base area of the triangular prism:
Base Area = (1/2) x A x B
Base Area = (1/2) x 4 ft x 8 ft
Base Area = 16 ft²
The height of the prism is given as the length of the opening, which is 24 ft.
Now we can calculate the volume:
Volume = Base Area x Height
Volume = 16 ft² x 24 ft
Volume ≈ 384 ft³
Therefore, the space contained within the goal is approximately 384 cubic feet.