Área do Prisma - Brasil Escola

Summary

In this video lesson, Pedro Ítalo, a mathematics teacher, explains how to calculate the total surface area of a prism. He introduces the concept of prisms, their bases, and lateral areas, providing clear examples. Through two detailed exercises, he demonstrates how to apply these concepts to real-world scenarios, such as calculating the amount of rubber needed to cover an Olympic-sized swimming pool and determining the lateral area of a box with a square base. The lesson emphasizes the formula: Total Area = 2 x Base Area + Lateral Area, making it easy to apply to various shapes of prisms.

Takeaways

• 😀 A prism is a polyhedron with two parallel and congruent bases. The lateral faces are polygons.
• 😀 The total area of a prism is calculated as twice the area of the base plus the lateral area.
• 😀 The formula for calculating the total area of a prism is: Total Area = 2 * Area of Base + Lateral Area.
• 😀 The area of the base depends on the shape of the base, whether it's triangular, square, pentagonal, etc.
• 😀 To calculate the area of a prism's base, multiply the length and width for rectangular bases or use appropriate formulas for other shapes.
• 😀 The lateral area is the area of the faces around the base, and it can be calculated by multiplying the perimeter of the base by the height of the prism.
• 😀 A real-world example is a swimming pool shaped like a rectangular parallelepiped, where you would calculate the area of the base and lateral surfaces to determine the amount of material needed to cover it.
• 😀 For a rectangular pool, the area of the base is found by multiplying the length and width, while the lateral area is calculated by multiplying the perimeter of the base by the height of the pool.
• 😀 Another example discusses a cardboard box with a square base. The volume of the box is found by multiplying the area of the square base by the height.
• 😀 The lateral area of the cardboard box is calculated by multiplying the perimeter of the square base by the height and then multiplying by the number of lateral faces (4 for a square base).

Q & A

What is a prism?

A prism is a polyhedron that has two parallel and congruent bases. The sides of a prism are formed by rectangles, and the shape of the base determines the type of the prism.

What is the formula to calculate the total surface area of a prism?

The total surface area of a prism is calculated using the formula: Total Surface Area (AT) = 2 × Area of the Base (AB) + Lateral Area (AL).

What is a polyhedron?

A polyhedron is a three-dimensional geometric figure whose faces are polygons. The faces are flat and meet at edges and vertices.

What shapes can the base of a prism have?

The base of a prism can be any polygon, such as a triangle, square, pentagon, etc. The shape of the base determines the specific type of the prism (e.g., triangular prism, cubic prism, pentagonal prism).

In the example of the Olympic swimming pool, how do we calculate the amount of rubber needed for the pool?

To calculate the amount of rubber needed for the pool, you need to calculate the area of the base and the lateral area of the pool. The total area to be covered is the base area plus the lateral area, excluding the top.

What is the formula for the volume of a prism?

The volume of a prism is calculated by multiplying the area of the base by the height of the prism: Volume (V) = Area of the Base × Height.

How do you calculate the lateral area of a prism?

The lateral area of a prism can be calculated by finding the area of the rectangular faces that surround the prism. If the base has n sides, the lateral area is the perimeter of the base multiplied by the height of the prism.

How would you find the height of a prism if you know the volume?

To find the height of a prism, divide the volume of the prism by the area of the base. For example, if the volume is 288 cm³ and the area of the base is 36 cm², then the height would be 288 ÷ 36 = 8 cm.

What is the lateral area of a box with a square base of side 6 cm and height 8 cm?

The lateral area of a box with a square base is calculated by multiplying the perimeter of the base by the height. The perimeter of a square with side length 6 cm is 24 cm (6 × 4), and multiplying by the height of 8 cm gives a lateral area of 192 cm².

What does the formula for calculating the lateral area of a prism depend on?

The formula for the lateral area of a prism depends on the perimeter of the base and the height of the prism. The lateral area is found by multiplying the perimeter of the base by the height.