What is the surface area of the triangular prism 3cm 4cm 5cm 11cm
To find the surface area of a triangular prism, we need to calculate the area of each face and then add them up.
First, let's find the area of the triangular bases. The base of the prism is a triangle with sides measuring 3 cm, 4 cm, and 5 cm. To find the area of a triangle, you can use Heron's formula:
s = (a + b + c) / 2
Area = √(s * (s - a) * (s - b) * (s - c))
where a, b, and c are the side lengths of the triangle, and s is the semiperimeter.
In this case:
s = (3 + 4 + 5) / 2 = 6
Area = √(6 * (6 - 3) * (6 - 4) * (6 - 5)) = √(6 * 3 * 2 * 1) = √(36) = 6 cm^2
Now, let's find the lateral surface area. The lateral surface area consists of three rectangles:
1. Rectangle with sides equal to the base of the prism:
Area = 5 * 11 = 55 cm^2
2. Two rectangles with sides equal to the height of the prism (which is 4 cm) and the other two sides are the sides of the base triangle (3 cm and 4 cm):
Area = 2 * 4 * 3 + 2 * 4 * 5 = 24 + 40 = 64 cm^2
Now, we can sum up all these areas to find the total surface area:
Total surface area = 2 * Area of base triangle + Lateral surface area
Total surface area = 2 * 6 + 55 + 64 = 12 + 55 + 64 = 131 cm^2
Therefore, the surface area of the triangular prism with side lengths 3 cm, 4 cm, 5 cm, and height 11 cm is 131 cm^2.