What is the surface area of the triangular prism s1 3cm. S2 4cm. S3 5cm. 11cm leanght
To find the surface area of a triangular prism, you first need to find the areas of the two triangular bases and the three rectangular sides.
Given:
s1 = 3 cm
s2 = 4 cm
s3 = 5 cm
length (l) = 11 cm
1. Area of the triangular base:
To find the area of a triangle, you can use the formula:
Area = (base * height) / 2
For s1, the base is 3 cm and height is unknown.
For s2, the base is 4 cm and height is unknown.
Let's find the height for each triangle using the Pythagorean theorem.
For s1:
3^2 = h^2 + 2^2
9 = h^2 + 4
h^2 = 5
h = √5 cm (approx. 2.24 cm)
For s2:
4^2 = h^2 + 2^2
16 = h^2 + 4
h^2 = 12
h = √12 cm (approx. 3.46 cm)
Now, we can find the areas of the two triangles:
Area of s1 = (3 * √5) / 2 cm^2 ≈ 3.36 cm^2
Area of s2 = (4 * √12) / 2 cm^2 ≈ 6.93 cm^2
2. Area of the three rectangular sides:
The three sides of the prism are rectangles with dimensions s1, s2, and s3.
Area of each rectangular side = length * width
Area of the first rectangular side = 3 * 11 = 33 cm^2
Area of the second rectangular side = 4 * 11 = 44 cm^2
Area of the third rectangular side = 5 * 11 = 55 cm^2
3. Total surface area:
Add the areas of the two triangular bases and the three rectangular sides to get the total surface area of the triangular prism:
Total surface area = (2 * (Area of s1 + Area of s2)) + (Area of 1st rectangle + Area of 2nd rectangle + Area of 3rd rectangle)
Total surface area = (2 * (3.36 + 6.93)) + (33 + 44 + 55)
Total surface area = (2 * 10.29) + 132
Total surface area = 20.58 + 132
Total surface area ≈ 152.58 cm^2
Therefore, the surface area of the triangular prism with side lengths of 3 cm, 4 cm, 5 cm, and a length of 11 cm is approximately 152.58 cm^2.