A triangular prism has an equilateral triangle as its base. The base of the triangle is 10cm and its height is 10cm. The length of the prism is also 10cm.
Find it's surface area
area of equilateral triangle of side s is
a = 1/2 s s√3/2 = 1/4 s^2 √3
so your prism has two bases and 3 faces
area = 2(1/4 *10^2 √3) + 3(10*10) = 300+50√3
To find the surface area of a triangular prism, you need to calculate the areas of all the individual faces and add them up.
In this case, the triangular prism has two triangular faces and three rectangular faces.
1. Triangular faces: Since the base of the triangular prism is an equilateral triangle, all three sides have equal lengths of 10 cm. To find the area of one triangle, you can use the formula for the area of an equilateral triangle:
Area = (sqrt(3) / 4) * side length^2
So, Area = (sqrt(3) / 4) * (10 cm)^2
= (sqrt(3) / 4) * 100 cm^2
= (1.732 / 4) * 100 cm^2
≈ 43.3 cm^2
Since there are two triangular faces, the total area of both is 2 * 43.3 cm^2 = 86.6 cm^2.
2. Rectangular faces: The three rectangular faces of the prism have dimensions 10 cm (length) x 10 cm (height). To find the area of each face, use the formula for the area of a rectangle:
Area = length * height
So, the area of one face = 10 cm * 10 cm = 100 cm^2.
Since there are three rectangular faces, the total area of all three is 3 * 100 cm^2 = 300 cm^2.
Finally, to find the total surface area of the prism, add the areas of all the faces:
Surface Area = 86.6 cm^2 (triangular faces) + 300 cm^2 (rectangular faces)
= 386.6 cm^2
Therefore, the surface area of the triangular prism is approximately 386.6 cm^2.