What is the surface area of a triangular prism with a base of 3 a height of 2.6 and a length of 7?
there are two triangular bases of area (1/2)*3*2.6
there are three rectangular faces. One has area 12*3
the other two have length 12, but we do not know the other two sides of the triangle...
To find the surface area of a triangular prism, you need to calculate the areas of its faces and then sum them up.
A triangular prism has two triangular faces and three rectangular faces. The formulas to calculate the area of each face are:
1. The area of a triangle = 0.5 * base * height
2. The area of a rectangle = length * width
Let's begin by calculating the areas of the triangular faces:
1. The base of the triangles is the base of the prism, which is given as 3.
2. The height of the triangles is the height of the prism, which is given as 2.6.
Using the formula for the area of a triangle:
Area of a triangle = 0.5 * base * height
Area of the triangular face = 0.5 * 3 * 2.6
Calculating this, we get:
Area of the triangular face = 3.9
Next, let's calculate the areas of the rectangular faces:
1. The length of the rectangular faces is the length of the prism, which is given as 7.
2. The width of the rectangular faces is the same as the base of the triangular faces, which is given as 3.
Using the formula for the area of a rectangle:
Area of a rectangle = length * width
Area of each rectangular face = 7 * 3
Calculating this, we get:
Area of each rectangular face = 21
Since there are three rectangular faces, to find the total area, we need to add up the areas of all five faces of the prism:
Total surface area = 2 * area of the triangular face + 3 * area of each rectangular face
Total surface area = 2 * 3.9 + 3 * 21
Calculating this, we get:
Total surface area = 7.8 + 63
Total surface area = 70.8
Therefore, the surface area of the given triangular prism is 70.8 square units.