PRISMAS EM 10 MINUTOS | ÁREA e VOLUME

Introduction

In this tutorial, you will learn how to calculate the area of the base, total area, and volume of prisms. This guide follows the easy-to-understand Method Curió, designed to help you master these concepts quickly and effectively.

Step 1: Understanding Prisms

• A prism is a three-dimensional shape with two parallel bases that are congruent.
• Common types of prisms include rectangular, triangular, and pentagonal prisms.
• To work with prisms, you need to know the shape of the base and the height of the prism.

Step 2: Calculating the Area of the Base

• Identify the shape of the base.
• Use the appropriate formula based on the shape:
  • Rectangle: Area = length × width
  • Triangle: Area = (base × height) / 2
  • Other shapes: Refer to specific area formulas for shapes like circles or polygons.

Example Calculation

• For a rectangular base with a length of 5 cm and a width of 3 cm:
  • Area = 5 cm × 3 cm = 15 cm²

Step 3: Calculating the Total Surface Area

• The total surface area of a prism can be calculated using the formula:
  • Total Surface Area = (Area of Base × 2) + (Perimeter of Base × Height)
• First, calculate the perimeter of the base shape:
  • Rectangle: Perimeter = 2(length + width)
  • Triangle: Perimeter = sum of all sides

Example Calculation

• Continuing with the previous rectangular example:
  • Perimeter = 2(5 cm + 3 cm) = 16 cm
  • Total Surface Area = (15 cm² × 2) + (16 cm × height)
  • If height is 4 cm, Total Surface Area = 30 cm² + 64 cm = 94 cm²

Step 4: Calculating the Volume

• The volume of a prism is calculated with the formula:
  • Volume = Area of Base × Height
• Use the area calculated in Step 2 and multiply it by the height of the prism.

Example Calculation

• Using the area from the rectangular base:
  • Volume = 15 cm² × 4 cm = 60 cm³

Conclusion

You now have the tools to calculate the area of the base, total surface area, and volume of prisms. Remember to:

• Identify the shape of the base for accurate calculations.
• Use the corresponding formulas for area, perimeter, and volume.

To further enhance your understanding of prisms, consider practicing with different shapes and dimensions.