What are perimeter and area?

Perimeter and area are fundamental concepts in geometry, essential for measuring the size and boundaries of various shapes.

Perimeter

Perimeter is the total length of the boundary of a two-dimensional shape.

Types of geometrical shapes:

• Polygons (e.g., triangles, rectangles, squares): Perimeter is the sum of the lengths of all sides.
• Circles: Perimeter is referred to as the circumference.

Rules for Solving Perimeter Problems:

Triangles:

• Sum of all three sides.
• Formula: P = a + b + c

Rectangles and Squares:

• Perimeter of rectangle is sum of all four sides: P = 2(l + w)
• Perimeter of square is four time of one side length: P = 4s
• Perimeter of circle is C = 2πr or C = πd where r is the radius and d is the diameter.

Area

Area is the measure of the space enclosed within a two-dimensional shape.

Types of areas:

Polygons:

• Area calculation depends on the shape (e.g., triangles, rectangles, squares).

Circles:

• Area is calculated using the radius.

Rules for Solving Area Problems:

• Formula of triangles area: A = $\frac{1}{2}$ * base * heights
• Formula of rectangles area: A = length * width
• Formula of square area: A = side ²
• Formula of circles area: A = πr ²

Quizzes:

1. A rectangular garden measures 15 meters in length and 10 meters in width. Calculate the perimeter.

2.A triangular plot of land has a base of 20 meters and a height of 10 meters. Calculate the area.

3. A circular swimming pool has a radius of 7 meters. Calculate the circumference.

4. A square park has a side length of 25 meters. Calculate the area.

5. A rectangular playground (30 meters by 20 meters) has a semicircular area (radius 10 meters) attached at one end. Calculate the total perimeter and area.

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