ÁREA DAS PRINCIPAIS FIGURAS PLANAS | GEOMETRIA PLANA

Dicasdemat Sandro Curió

25 Feb 202021:13

Summary

TLDRThis educational video focuses on calculating the areas of various plane figures commonly found in entrance exams. It covers the area formulas for shapes like squares, rectangles, trapezoids, rhombuses, triangles, parallelograms, and circles, providing clear, step-by-step examples. The host explains the importance of understanding key geometric principles, such as using Pythagoras' theorem for determining unknown sides, and how to use provided data like diagonals or perimeter. The video emphasizes both theoretical explanations and practical problem-solving methods to help viewers improve their geometry skills for exams.

Takeaways

😀 Understanding geometric areas: The script discusses the formulas for calculating the area of various plane figures, including squares, rectangles, trapezoids, rhombuses, triangles, parallelograms, and circles.
😀 Square area formula: The area of a square is calculated by squaring the length of its side (side × side).
😀 Rectangle area formula: The area of a rectangle is calculated by multiplying the base by the height (base × height).
😀 Trapezoid area formula: The area of a trapezoid is calculated by averaging the lengths of the two bases and multiplying by the height ((base1 + base2) / 2 × height).
😀 Rhombus area formula: The area of a rhombus is the product of its diagonals divided by two (diagonal1 × diagonal2 / 2).
😀 Triangle area formula: The area of a triangle is calculated as base × height divided by 2 (base × height / 2).
😀 Parallelogram area formula: The area of a parallelogram is the base times the height (base × height).
😀 Circle area formula: The area of a circle is calculated as pi times the square of the radius (π × radius²).
😀 Importance of correct units: When calculating areas, it's essential to include the correct units, such as square centimeters for area.
😀 Pitágoras’ Theorem for unknown sides: The script uses the Pythagorean theorem to solve for missing sides in right triangles, which helps in finding areas of figures like rectangles and trapezoids.
😀 Example application of formulas: The script provides specific problems, such as calculating the area of a square with a diagonal and solving for the area of a trapezoid given various dimensions, demonstrating practical use of these formulas.

Q & A

What is the area formula for a square?
-The area of a square is calculated by multiplying the side length by itself, or 'side x side'.
How is the area of a rectangle calculated?
-The area of a rectangle is calculated by multiplying its base by its height, or 'base x height'.
What is the formula for the area of a trapezoid?
-The area of a trapezoid is calculated as the average of the lengths of the two bases (base1 + base2) divided by 2, then multiplied by the height, or '((base1 + base2) / 2) x height'.
How do you calculate the area of a rhombus?
-The area of a rhombus is calculated by multiplying its two diagonals and dividing the result by 2, or 'diagonal1 x diagonal2 / 2'.
What is the formula for the area of a triangle?
-The area of a triangle is calculated by multiplying the base by the height and dividing the result by 2, or '(base x height) / 2'.
How is the area of a parallelogram determined?
-The area of a parallelogram is calculated by multiplying the base by the height, or 'base x height'.
What is the area formula for a circle?
-The area of a circle is calculated as pi multiplied by the square of the radius, or 'π x r²'.
How do you calculate the diagonal of a square?
-The diagonal of a square is calculated by multiplying the side length by the square root of 2, or 'side x √2'.
How do you find the height of a right-angled triangle using Pythagoras' Theorem?
-To find the height (or one leg) of a right-angled triangle, you use Pythagoras' Theorem: 'a² + b² = c²', where 'a' and 'b' are the legs and 'c' is the hypotenuse.
How is the area of a trapezoid calculated when the height is missing?
-If the height of a trapezoid is missing, it can be found using Pythagoras' Theorem, depending on the available measurements of the sides and the bases.