Math Problem Statement

Keliling: The problem asks to find the perimeter of a square with side length 20 and possibly the circumference of the circle in which the square is inscribed.

Solution

The image shows a square inscribed within a circle with the label "Keliling" which means "perimeter" in Indonesian. The side length of the square is given as 20 units. The task appears to be finding the perimeter (keliling) of the square or possibly the circumference of the circle.

Let's solve both parts for clarity:

  1. Perimeter of the Square:

    • The perimeter PP of a square is given by P=4×side lengthP = 4 \times \text{side length}.
    • Here, the side length = 20 units.
    • P=4×20=80P = 4 \times 20 = 80 units.
  2. Circumference of the Circle:

    • Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.
    • The diagonal dd of a square with side length ss is given by d=s2d = s\sqrt{2}.
    • Here, s=20s = 20 units, so d=202d = 20\sqrt{2}.
    • The circumference CC of a circle is given by C=π×diameterC = \pi \times \text{diameter}.
    • C=π×20288.83C = \pi \times 20\sqrt{2} \approx 88.83 units.

Summary

  • Perimeter of the square: 8080 units.
  • Circumference of the circle: Approximately 88.8388.83 units.

Would you like to know more details or have any questions about this problem?

Related Questions:

  1. What is the area of the square with a side length of 20 units?
  2. How do you calculate the diagonal of a square?
  3. What is the area of the circle inscribed around a square with a side length of 20 units?
  4. How is the radius of the circle related to the side length of the square?
  5. How do you find the circumference of a circle given its diameter?

Tip:

When dealing with a square inscribed in a circle, remember that the circle's diameter is the diagonal of the square.

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Math Problem Analysis

Mathematical Concepts

Geometry
Perimeter
Circumference
Diagonals
Squares
Circles

Formulas

Perimeter of square P = 4 * side length
Diagonal of square d = side length * sqrt(2)
Circumference of circle C = π * diameter

Theorems

Pythagorean Theorem (for diagonal of a square)

Suitable Grade Level

Grades 6-8