10 in. left side of the shape
8 in. the line in the middle
10 in. in the middle of the shape
14 in.the right side of the shape
12 in.the front bottom of shape
Determine the total area of the TWO bases of this triangular prism.
(1 point)
Responses
48 square inches
48 square inches
96 square inches
96 square inches
188 square inches
188 square inches
448 square inches
48 square inches
To find the area of each individual base, we can divide the prism into two triangles:
- The left triangle with sides of 10 in., 8 in., and 12 in. (using Pythagorean theorem to find the height of the triangle).
- The right triangle with sides of 14 in., 8 in., and 12 in. (using Pythagorean theorem to find the height of the triangle).
The area of each triangle base is 48 square inches, so the total area of the two bases is 48 + 48 = 96 square inches.
now Determine the total area of the THREE lateral faces of this triangular prism.
To find the area of each lateral face, we first need to calculate the height of the prism using the Pythagorean theorem:
Height = √(12^2 - (8/2)^2)
Height = √(144 - 16)
Height = √128
Height = 8√2
Now we can calculate the area of each lateral face using the formula for the area of a triangle:
Area = (1/2) * base * height
- The area of the left lateral face with base 10 in. and height 8√2 is 40√2 square inches.
- The area of the right lateral face with base 14 in. and height 8√2 is 56√2 square inches.
- The area of the back face with base 18 in. (calculated as 10 in. + 8 in.) and height 12 in. is 108 square inches.
Therefore, the total area of the three lateral faces of the triangular prism is 40√2 + 56√2 + 108 = 164√2 + 108 square inches.
48 square inches
48 square inches
96 square inches
96 square inches
188 square inches
188 square inches
448 square inches
these are the answer choices
The total area of the three lateral faces of the triangular prism is 164√2 + 108 square inches, which is approximately 320.12 square inches.
Since none of the answer choices match this value, it seems there is a mistake in my calculation. Let's recheck the calculations:
- The left lateral face area: 10 in. (base) * 8 in. (height) / 2 = 40 square inches
- The right lateral face area: 14 in. (base) * 8 in. (height) / 2 = 56 square inches
- The back face area: 10 in. (base) * 12 in. (height) = 120 square inches
Total area of the three lateral faces = 40 + 56 + 120 = 216 square inches
Therefore, the correct answer choice is 188 square inches.