Umfang Und Flächeninhalt Aufgaben Klasse 8

In geometry, the area of a shape is the amount of two-dimensional space that the shape occupies. Area is measured in square units, such as square centimeters (cm²) or square inches (in²).

The area of a shape can be found by counting the number of square units that the shape covers. For example, the figure below shows a shape with an area of 9 square units.

To find the area of more complex shapes, we can use a formula. For example, the formula for the area of a rectangle is:

Area of a rectangle = length x width

Let’s try an example. Find the area of the rectangle below.

To solve this problem, we first need to identify the length and width of the rectangle. The length is the longest side and is represented by the letter l. The width is the shorter side and is represented by the letter w.

In this example, the length is 6 and the width is 4. We can plug these values into the formula and solve for the area.

Area = l x w Area = 6 x 4 Area = 24

Therefore, the area of the rectangle is 24 square units.

There are other formulas for finding the area of different shapes. For example, the formula for the area of a triangle is:

Area of a triangle = 1/2 x base x height

The base is the length of the triangle’s bottom side and the height is the perpendicular distance from the base to the triangle’s apex (pointy top).

Let’s try an example. Find the area of the triangle below.

To solve this problem, we first need to identify the base and height of the triangle. The base is the bottom side of the triangle and is represented by the letter b. The height is the perpendicular distance from the base to the triangle’s apex and is represented by the letter h.

In this example, the base is 6 and the height is 4. We can plug these values into the formula and solve for the area.

Area = 1/2 x b x h Area = 1/2 x 6 x 4 Area = 12

Therefore, the area of the triangle is 12 square units.

Aufgaben mit Lösungen Umfang Und Flächeninhalt Klasse 8

In diesem Artikel findest du mehrere Übungen mit Schritt-für-Schritt-Lösungen zum Thema Umfang und Flächeninhalt. Ideal für die Vorbereitung auf eine Klassenarbeit oder eine Prüfung.

Übung 1

Berechne den Umfang und den Flächeninhalt des Quadrates mit der Seitenlänge a = 8 cm.

Lösung:
Umfang = 4a = 4 * 8 cm = 32 cm
Flächeninhalt = a² = 8² cm² = 64 cm²

Übung 2

Berechne den Umfang und den Flächeninhalt der Rechtecke mit den Seitenlängen a = 5 cm und b = 3 cm.

Lösung:
Umfang = 2a + 2b = 2 * 5 cm + 2 * 3 cm = 16 cm
Flächeninhalt = a * b = 5 cm * 3 cm = 15 cm²

Übung 3

Berechne den Umfang und den Flächeninhalt des Dreiecks mit den Seitenlängen a = 4 cm, b = 6 cm und c = 7 cm.

Lösung:
Umfang = a + b + c = 4 cm + 6 cm + 7 cm = 17 cm
Flächeninhalt = ½ * a * b * sin(C) = ½ * 4 cm * 6 cm * sin(7°) ≈ 11,4 cm²

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