Area and perimeter are two fundamental concepts in geometry. The area of a shape is the amount of space inside the shape. The perimeter is the total length of the shape’s sides. Each geometric shape has its own area and perimeter formulas. In this article, we will go through step-by-step how to calculate the area and perimeter of basic geometric shapes.
Step 1: Basic Geometric Shapes and Their Formulas Square: The area of a square is the length of one side squared (Area = a2). The perimeter is 4 times the length of one side (Perimeter = 4a).
Rectangle: The area of a rectangle is length x width (Area = length x width). The perimeter is 2 x (length + width) (Perimeter = 2x(length + width)).
Triangle: The area of a triangle is base x height / 2 (Area = base x height / 2). The perimeter is the sum of its 3 sides (Perimeter = a + b + c).
Step 2: Simple Example Problems A square has sides of length 4 cm. What are its area and perimeter? Area = a2 = 42 = 16 cm2 Perimeter = 4a = 4 x 4 = 16 cm
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More Example
A rectangle has a length of 10 cm and a width of 5 cm. What are its area and perimeter in cm2 and cm? Area = length x width = 10 x 5 = 50 cm2 Perimeter = 2x(length + width) = 2x(10 + 5) = 2×15 = 30 cm
A rectangular garden has a length of 12 yards and a width of 8 yards. A sidewalk of uniform width will be constructed around the garden. If the total area enclosed by the garden and sidewalk is 192 square yards, what is the width of the sidewalk?
To solve:
- The area of the garden is: Length x Width 12 x 8 = 96 square yards
- The total area is 192 square yards
- The area of the garden is 96 square yards
- So the additional area enclosed by the sidewalk must be: Total area – Garden area 192 – 96 = 96 square yards
- This additional 96 square yards is the area of the sidewalk
- The sidewalk goes around the entire perimeter of the garden
- The perimeter of the garden is: 2x(Length + Width) 2x(12 + 8) = 2×20 = 40 yards
- Let’s call the width of the sidewalk x
- The area of the sidewalk is equal to its width x the perimeter of the garden x * 40 = 96
- Solve to find x = 2.4 yards
Therefore, the width of the sidewalk is 2.4 yards.
This demonstrates a more complex, multi-step area and perimeter problem with a real-world application.
We have now learned the concepts of area and perimeter step-by-step, starting from simple to more complex examples. It is important to write the formulas correctly and substitute the values appropriately when solving each problem. Practicing many exercises helps reinforce these concepts!
