FÁCIL E RÁPIDO | ÁREA DO TRIÂNGULO - GEOMETRIA

Summary

This video tutorial explains how to calculate the area of a triangle using the formula: Area = (Base × Height) / 2. The presenter walks through examples, including right triangles and various triangle types, highlighting key points like the importance of perpendicular height. The video also covers solving for unknowns, such as height, when the area is given. It offers practical tips, including simplifying fractions and applying cross-multiplication, ensuring viewers grasp both the formula and its application for geometry problems in exams. A final motivational note encourages engagement and sharing the video.

Takeaways

• 😀 The area of any triangle can be calculated using the formula: base × height ÷ 2.
• 😀 The height of a triangle is always perpendicular to the base, forming a right angle.
• 😀 For a right triangle, the area can also be calculated by multiplying the lengths of the two legs (catetos) and dividing by 2.
• 😀 If two congruent triangles are placed together, they form a rectangle. Therefore, the area of the triangle is half of the rectangle's area.
• 😀 The area formula for any triangle is based on its base and height, regardless of the triangle's type.
• 😀 The area of a right triangle with legs measuring 8 cm and 7 cm is 28 cm² (8 × 7 ÷ 2).
• 😀 When solving problems, always remember to include the correct units for the area (e.g., cm² for centimeters squared).
• 😀 A triangle's area problem may give additional information, such as the area, and ask for the missing height or base.
• 😀 In problems where the area and base are given, use algebra to solve for the unknown height or base. For example, if the area is 60 cm² and the base is 12 cm, solve for the height.
• 😀 In an example, the area equation 12 × x ÷ 2 = 60 can be simplified and solved by multiplying crosswise, leading to the height of 10 cm.
• 😀 The video emphasizes the importance of practicing with various triangle problems to fully understand the concept of area.

Q & A

What is the formula for calculating the area of a triangle?

The area of a triangle is calculated using the formula: Area = (Base × Height) / 2.

What does the height of a triangle represent?

The height of a triangle is the perpendicular distance from the base to the opposite vertex, forming a 90-degree angle with the base.

In the example with a right triangle, how was the area calculated?

In the right triangle example, the area was calculated using the formula: Area = (Base × Height) / 2. The base and height were given as 8 cm and 7 cm, respectively. The area = (8 × 7) / 2 = 28 cm².

What is the significance of the right triangle example in the video?

The right triangle example helps to demonstrate that the area of a triangle is half the area of a rectangle with the same base and height.

How do you calculate the area of a triangle if you know the base and height?

To calculate the area of a triangle, simply multiply the base by the height, then divide by 2.

How is the area formula for a triangle applied when the base and height are given in the script?

In the example with a base of 10 cm and height of 9 cm, the area is calculated as: Area = (10 × 9) / 2 = 45 cm².

What unit is used for the area of a triangle?

The area of a triangle is measured in square units, such as cm² (centimeters squared), depending on the units used for the base and height.

How do you find the height of a triangle if the area and base are known?

To find the height, rearrange the area formula: Height = (Area × 2) / Base. For example, if the area is 60 cm² and the base is 12 cm, the height is (60 × 2) / 12 = 10 cm.

What is the role of the perpendicularity of the height in calculating the area?

The height must be perpendicular to the base because the formula for the area of a triangle relies on this 90-degree angle to correctly measure the distance from the base to the vertex.

What does the video teach about calculating the area of an equilateral triangle?

The video mentions that the area of an equilateral triangle is a common geometry problem but does not go into details. It focuses on general triangles with known base and height.