The surface area of a triangular prism. The base is a right triangle with base 1 foot, height 2 feet and third side 2 point 2 feet. The height of the prism is 3 feet.
2 + 3 (1 + 2 + 2.2)
If your base is 1 ft, by 2 ft, by 2.2 ft, it is NOT a right angled triangle
1^2 + 2^2 ≠ 2.2^2
check your question or your typing
Where is the vertex of the pyramid in relation to the base?
That will affect the slant heights of the faces.
IF it is a right-angled triangle with base 1 and height of 2, then we
need to find the third side.
Make a sketch of a triangle with base 1 and side of 2.2, draw a
perpendicular from the end of the 2.2 to the base, label it height = 2
Let A be the vertex of segment 2.2 and the base 1
sin A = 2/2.2 = .9090...
angle A = 65.38°
thirdside^2 = 1^2 + 2.2^2 - 2(1)(2.2)cos 65.38
= 4.007
third side = √4.007 = 2.002
So for all practical purposes, R_scott's answer is correct
To find the surface area of a triangular prism, we need to find the areas of all the surfaces and add them together.
In this case, the triangular prism has two triangular bases and three rectangular faces.
To find the area of the triangular bases, we can use the formula for the area of a triangle:
Area = (base * height) / 2
Given that the base of the right triangle is 1 foot and the height is 2 feet, we can calculate the area of the base:
Base Area = (1 * 2) / 2 = 1 square foot
Since there are two triangular bases, the total area of the triangular bases is 2 square feet.
Next, we need to find the areas of the three rectangular faces. To calculate the area of a rectangle, we use the formula:
Area = length * width
The length of each rectangular face is the same as the height of the prism, which is given as 3 feet. The width is the same as the length of the base of the triangle.
The first rectangular face has a length of 3 feet and a width equal to the base of the triangle, which is 1 foot. Therefore, the area of the first rectangular face is:
First Rectangular Face Area = 3 * 1 = 3 square feet
The second rectangular face also has a length of 3 feet, but its width is equal to the third side of the base triangle, which is 2.2 feet. So, the area of the second rectangular face is:
Second Rectangular Face Area = 3 * 2.2 = 6.6 square feet
Similarly, the third rectangular face has a length of 3 feet and a width equal to the base of the triangle, which is 1 foot. Thus, the area of the third rectangular face is:
Third Rectangular Face Area = 3 * 1 = 3 square feet
Summing up all the areas, we get:
Total Surface Area = 2 (Triangular Bases) + 3 (Rectangular Faces)
= 2 + 3 + 6.6 + 3
= 14.6 square feet
Therefore, the surface area of the given triangular prism is 14.6 square feet.