Formula for calculating the area of a rectangular box

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3. Types of exercises on the lateral area and total area of a rectangular prism

In this article, Mytour will share the formula for calculating the area of a rectangular box along with related exercises and solutions to help you enhance your mathematical knowledge and effectively tackle exercises. Regular practice helps you remember the formula and apply it flexibly.

You can review and practice the knowledge of calculating the area of a rectangular box through the theoretical system and practical exercises compiled below.

Formula for calculating the area of a rectangular box

S_total = 2h.(a + b)

+ In simple terms: The lateral surface area of a rectangular box is the product of its height and the sum of the lengths of its adjacent sides.

- Formula for calculating the total surface area of a rectangular box:

S_total = S_lateral + 2ab = 2h.(a+b) + 2ab

+ In simple terms: The total surface area of a rectangular box is the sum of its lateral surface area and the area of the two remaining faces.

- Explanation of symbols: S_lateral represents the lateral surface area of the rectangular box

where a and b are respectively the length and width, and h is the height of the rectangular box.

- Area units: measured in square units, such as m2 (square meters), cm2 (square centimeters)

Once you have found Sxq, you can determine h:

h = Sxq:[2(a+b)] = (S - 2ab):[2(a+b)]

- Calculate the diagonal of the rectangular prism:

3. Types of exercises on the lateral area and total area of a rectangular prism

Exercise 1: Calculate the lateral area and total area of the rectangular prism, given:

a) Length 20 m, width 10 m, height 7 m
b) Length 7/3 cm, width 5/3 cm, height 2/3 cm
c) Length 6.8 dm, width 3.4 dm, height 2.1 dm
d) Length 15 cm, width 5 cm, height 3 cm

Exercise 2: A rectangular box has a height of 2.3 cm, a length of 5.4 cm, and a width of 3 cm. Asking:

a) What is the lateral area of the box?
b) What is the total area of the box?

Problem 3: A rectangular water tank has a length of 7 m, a width equal to half the length, and a height of 1.5 m. Calculate the lateral area and total area of the tank.
Problem 4: A rectangular classroom is 7.8m long, 6.2m wide, and 4.3m high needs to be painted on walls and ceiling. Calculate the area needed for painting the room given the total area of the doors is 8.1 m².

Guidelines for solving the exercises

Exercise 1: You tackle this exercise by applying the two formulas for calculating the area of a rectangular prism mentioned above.
Exercise 2: Similarly to exercise 1, use the formulas for calculating the total area and lateral area.

Problem 3: Solve this exercise as follows:

- Step 1: Find the width of the water tank
- Step 2: Find the lateral area and total area using the given formulas.

Problem 4:

* Procedure: Excluding the door area, the lateral area of the classroom is simply the lateral area of the rectangular prism with the dimensions given in the problem.
- The area needed for painting the classroom will be the sum of the lateral area (excluding the door area) plus the area of one base (ceiling).

- The area needed for painting the classroom will be equal to the area needed for painting around (excluding the door area) plus the area of one base (ceiling).

* Sample solution:

The lateral area of the classroom is:

2 x 4.3 x (7.8 + 6.2) = 120.4 (m²)

The ceiling area of the classroom is:

7.8 x 6.2 = 48.36 (m²)

The area needed for painting that classroom is:

(120.4 + 48.36) - 8.1 = 160.66 (m²)

Answer: 160.66 (m²)

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Frequently Asked Questions

What is the formula for calculating the lateral surface area of a rectangular box?

The formula for calculating the lateral surface area of a rectangular box is Stotal = 2h.(a + b), where 'h' is the height, 'a' is the length, and 'b' is the width of the box.

How do you calculate the total surface area of a rectangular box?

To calculate the total surface area of a rectangular box, use the formula Stotal = Slateral + 2ab, which combines the lateral surface area and the area of the two remaining faces.

What units are used to measure the area of a rectangular box?

The area of a rectangular box is measured in square units, such as square meters (m²) or square centimeters (cm²). It is important to keep consistent units when performing calculations.

How can I determine the height of a rectangular box given its area?

To determine the height of a rectangular box from its area, you can rearrange the formula: h = (S - 2ab) / [2(a + b)], where 'S' is the total area, 'a' is the length, and 'b' is the width.

What steps are involved in calculating the lateral area and total area of a rectangular prism?

To calculate the lateral area and total area of a rectangular prism, apply the formulas for lateral surface area and total area using the dimensions provided. Ensure all units are consistent.