What si the volume and surface area of a triangular prism with the dimensions of a 2.5 base, 2.5 height, and 7 length
The volume, V of a triangular prism is
V=(1/2)(base*height of triangle)* height of prism
The surface area, S is given by:
S=(perimeter of base)*height of prism + base*height of triangle
Post your answers for checking if you wish.
To find the volume and surface area of a triangular prism, we need to use the formulas:
Volume = base area × height
Surface area = (2 × base area) + (base perimeter × height) + (2 × triangular lateral area)
First, let's find the base area of the triangular prism.
The base of the triangular prism is a triangle with a base of 2.5 and a height of 2.5.
Base Area = (base × height) / 2 = (2.5 × 2.5) / 2 = 6.25 / 2 = 3.125
Now, let's find the triangular lateral area. The triangular lateral area is the area of the two triangular faces on the sides of the prism.
Triangular Lateral Area = (base × height) / 2 = (2.5 × 2.5) / 2 = 6.25 / 2 = 3.125
Next, let's find the base perimeter. The base perimeter is the sum of the lengths of the three sides of the base triangle.
Base Perimeter = 2 × (base + height) = 2 × (2.5 + 2.5) = 2 × 5 = 10
Now, we can calculate the volume and surface area using the formulas mentioned earlier.
Volume = Base Area × Height = 3.125 × 7 = 21.875 cubic units
Surface Area = (2 × Base Area) + (Base Perimeter × Height) + (2 × Triangular Lateral Area)
= (2 × 3.125) + (10 × 7) + (2 × 3.125)
= 6.25 + 70 + 6.25
= 82.5 square units
Therefore, the volume of the triangular prism is 21.875 cubic units and the surface area is 82.5 square units.