Buzz
Rectangular Prism is a shape with 6 faces forming rectangles, 8 vertices, and 12 edges, intersecting at a single point. Everyday objects resembling rectangular prisms include bricks, cabinets, paper boxes, cartons, water tanks...
Formula for calculating the area of a rectangular prism.
HOW TO CALCULATE THE AREA OF A RECTANGULAR PRISM
When it comes to calculating the area of a rectangular prism, we need to consider both the lateral and total surface areas. The specific formulas for each type of area are as follows:
+ Lateral Surface Area: is the area of the four side faces: Lsa = 2(a+b).h
The lateral surface area of a rectangular prism is the product of the height and the perimeter of the base.
+ Total Surface Area: is the sum of the lateral surface area and the area of the two bases:
Tsa = Lsa + Base Area = 2(a+b).h + 2ab
Explanation of the variables in the formula:
Lsa: Lateral Surface Area
a,b: Length of the two base sides
h: Height of the rectangular prism
APPLYING THE FORMULA TO EXAMPLE EXERCISES
Some types of exercises related to calculating the area of a rectangular prism include:
- Given width, length, and height, calculate the surface area.
- Given width, length, and lateral surface area, find the height of the prism.
- Given width, length, lateral surface area, calculate the total surface area of the rectangular prism.
Example 1: Calculate the lateral and total surface area of a storage cabinet with dimensions: width 0.5m, length 1.2m, and height 2m.
Solution:
Applying the formulas for lateral and total surface area to this problem, we get the results:
The lateral surface area of the prism is: Lsa = 6.8 m2
The total surface area of the prism is:
Total surface area of the rectangular prism is: Tsa = Lsa + Base Area = 2(a+b).h + 2ab = 8 m2
Example 2: Determine the height of a water tank given that the tank has a length of 5m, width 2m, and a lateral surface area of 42 m2.
Solution:
The problem provides length a = 5m, width b = 2m, Sxq = 42 m2. Calculate the height h =?
From the formula for lateral surface area, we deduce that the height is given by:
Sxq = 2(a+b).h => h = Sxq : 2(a + b) = 42: 2 (5+2) = 3 m.
The result is a water tank with a height of 3m.
In general, problems related to area calculation are not overly complicated. Depending on the given conditions in each problem, you need to rely on the formula for the rectangular prism's area to deduce the calculation of other quantities.
Related to rectangular prisms, there are also problems involving volume calculation, diagonal length, etc. You can explore more articles on Mytour.vn for reference and geometry revision.
https://Mytour.vn/cach-tinh-dien-tich-hinh-hop-chu-nhat-25353n.aspx
A cube is a special case of a rectangular prism when all edges are equal. Therefore, the formula for cube surface area is similar to that of a rectangular prism: Lsa = 4a2, Tsa = 6a2.
