Prism Calculator

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A prism is a three dimensional geometrical figure have two parallel polygon faces at ends called bases and parallel lateral edges. Here we are dealing with two types of prisms namely Triangular prism and Rectangular Prism.

A triangular prism is a three sided prism that has a triangle on each end called bases and three rectangles on the sides.

A rectangular prism is a six sided prism with bases and faces consisting three pairs of congruent rectangles.

Prism Calculator calculates is a online tool which calculates the dimensions of the prism. Triangular prism Calculator calculates the base area, base perimeter, surface area and volume of the prism of triangular prism if length, base and height are entered and Rectangular Calculator also calculates diagonal of prism in additional to other dimensions of rectangular prism if length, width and height are entered.

Prism Formulas

Let us analyze the method of finding the parameters in triangular prism and rectangular prism.

Step 1 : Read the given problem and observe what are the dimension given?
1. If length, base, height and sides are given the prism is triangular
2. If length, width and height are given the given prism is rectangular.

Step 2 : If the triangular prism is given find the dimensions using formulas

• Area of base A = $\frac{1}{2}$ $\times$ l $\times$ b
• Perimeter of base P = S1 + S2 + S3
• Surface area of prism = lb + (S1 + S2 + S3)h
• Volume of prism = $\frac{1}{2}$ $\times$ l $\times$ w $\times$ h

• Where l = altitude or length, b = base and h = height

If the rectangular prism find the dimensions using formulas
1. Area of base = l $\times$ w
2. Perimeter of base P = (2l + 2w)
3. Surface area of prism = 2(lw) + (2l + 2w)h
4. volume of prism = l $\times$ w $\times$ h
5. Diagonal of prism = $\sqrt{l^2 + w^2 + h^2}$

Where l = length, w = width and h = height.
Put in the values in the above formulas and get the answer.

Prism Examples

Below are given some solved problems on prism which may be helpful for you.

Solved Examples

Question 1: Calculate the area of base, surface area, perimeter and volume of the triangular prism having altitude as 5cm, base as 6cm and height as 8cm respectively with equilateral sides of 4 cm.
Solution:

Step 1: The given parameters are side S1 = S2 = S3 = 4 cm, Altitude l = 5 cm, Base b = 6 cm, Height h = 8 cm

Step 2: The area of the base A = $\frac{1}{2}$ $\times$ l $\times$ b

= $\frac{1}{2}$ $\times$ 5 $\times$ 6

= 15 cm2.
The surface area of prism = lb + (S1 + S2 + S3) h
= 5 $\times$ 6 + (4 + 4 + 4) 8
= 126 cm2
The perimeter of the base P = S1 + S2 + S3
= 4 + 4 + 4 = 12 cm

The volume of the prism V = $\frac{1}{2}$ $\times$ a $\times$ b $\times$ h

= $\frac{1}{2}$ $\times$ 5 $\times$ 6 $\times$ 8

= 120 cm3.

Question 2: If a rectangular prism is having a length of 9 cm, width 5 cm and a height of 10 cm, Calculate the area of base, perimeter of base, surface area of prism, volume of the prism and diagonal of prism.
Solution:

Step 1: The given parameters are length l = 9 cm, Width w = 5 cm, Height h = 10 cm

Step 2: The area of the base A = l $\times$ w = 9 $\times$ 5 = 45 cm2
The Perimeter of base P = (2l + 2w) = (2 $\times$ 9 + 2 $\times$ 5) = 28 cm.
The Volume of the prism V = l $\times$ w $\times$ h = 9 $\times$ 5 $\times$ 10 = 450 cm3
The Diagonal of prism = $\sqrt{l^2 + w^2 + h^2}$ = $\sqrt{9^2 + 5^2 + 10^2}$ = $\sqrt{206}$ = 14.35 cm2.