Math Problem Statement

Tentukan keliling dari gambar di bawah ini!

10 points Captionless Image 154 cm 128 cm 140 cm 200 cm

Tentukan keliling dari gambar di bawah ini!

Solution

To find the perimeter (or keliling) of the figure, we need to consider the shapes involved separately: a semicircle and a rectangle.

Given Information

  • Rectangle dimensions: 31cm31 \, \text{cm} (length) and 17cm17 \, \text{cm} (width).
  • Semicircle: The diameter is 14cm14 \, \text{cm}, which implies a radius of 7cm7 \, \text{cm} (half of the diameter).

Steps to Calculate Perimeter

  1. Perimeter of the Rectangle (excluding one side):

    • Normally, the perimeter of a rectangle is 2×(length+width)2 \times (\text{length} + \text{width}).
    • However, we are excluding the 14 cm side (the diameter of the semicircle), so: Rectangle perimeter=31+17+17=65cm\text{Rectangle perimeter} = 31 + 17 + 17 = 65 \, \text{cm}
  2. Perimeter of the Semicircle:

    • The circumference of a full circle is 2πr2 \pi r.
    • For a semicircle, it would be πr\pi r plus the diameter (to include the straight edge).
    • Therefore: Semicircle perimeter=π×7+14=7π+14\text{Semicircle perimeter} = \pi \times 7 + 14 = 7\pi + 14
    • Using π3.14\pi \approx 3.14: Semicircle perimeter7×3.14+14=21.98+14=35.9836cm\text{Semicircle perimeter} \approx 7 \times 3.14 + 14 = 21.98 + 14 = 35.98 \approx 36 \, \text{cm}
  3. Total Perimeter: Total Perimeter=65+36=101cm\text{Total Perimeter} = 65 + 36 = 101 \, \text{cm}

The closest option to the calculated perimeter would need verification from additional problem constraints.

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Math Problem Analysis

Mathematical Concepts

Geometry
Perimeter

Formulas

Perimeter of a rectangle: 2 * (length + width)
Circumference of a circle: 2 * π * radius
Perimeter of a semicircle: π * radius + diameter

Theorems

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Suitable Grade Level

Grades 7-9