Вопрос:

Find the area and perimeter of the polygons.

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Ответ:

Figure 1:

This figure can be divided into two rectangles. A larger rectangle with dimensions 4 cm by 2 cm and a smaller rectangle with dimensions 3 cm by 2 cm.

  • Area of the larger rectangle: $$4 \times 2 = 8$$ cm2
  • Area of the smaller rectangle: $$3 \times 2 = 6$$ cm2
  • Total Area: $$8 + 6 = 14$$ cm2
  • Perimeter: $$4 + 2 + 3 + 2 + 1 + 4 = 16$$ cm

Note: The provided OCR has a handwritten calculation that says '27 cm²', which does not match the dimensions. The calculation here is based on the visible dimensions.

Figure 2:

This figure can be divided into two rectangles. A larger rectangle with dimensions 4 cm by 2 cm and a smaller rectangle with dimensions 4 cm by 2 cm.

  • Area of the first rectangle: $$4 \times 2 = 8$$ cm2
  • Area of the second rectangle: $$4 \times 2 = 8$$ cm2
  • Total Area: $$8 + 8 = 16$$ cm2
  • Perimeter: $$4 + 2 + 4 + 2 + 4 + 2 + 4 + 2 = 24$$ cm

Note: The provided OCR has handwritten calculations 'P=12cm' and 'S=16cm²', which seem to refer to a different shape or have an error in calculation/transcription.

Figure 3:

This figure can be divided into two rectangles. A larger rectangle with dimensions 5 cm by 3 cm and a smaller rectangle with dimensions 3 cm by 2 cm.

  • Area of the larger rectangle: $$5 \times 3 = 15$$ cm2
  • Area of the smaller rectangle: $$3 \times 2 = 6$$ cm2
  • Total Area: $$15 + 6 = 21$$ cm2
  • Perimeter: $$5 + 3 + 3 + 2 + 2 + 5 = 20$$ cm

Note: The provided OCR has handwritten calculations 'S=19cm²' and 'P=1344', which do not match the visible dimensions.

Figure 4:

This figure can be divided into two rectangles. A larger rectangle with dimensions 8 cm by 5 cm and a smaller rectangle with dimensions 3 cm by 2 cm.

  • Area of the larger rectangle: $$8 \times 5 = 40$$ cm2
  • Area of the smaller rectangle: $$3 \times 2 = 6$$ cm2
  • Total Area: $$40 + 6 = 46$$ cm2
  • Perimeter: $$5 + 8 + 2 + 3 + 5 + 3 = 26$$ cm

Note: The provided OCR has handwritten calculations 'S=27cm²' and 'P=26cm', where the perimeter matches but the area does not.

Figure 5:

This figure can be seen as a large rectangle with a smaller rectangle removed from one corner. The large rectangle has dimensions 8 cm by 8 cm, and the removed rectangle has dimensions 6 cm by 3 cm.

  • Area of the large rectangle: $$8 \times 8 = 64$$ cm2
  • Area of the removed rectangle: $$6 \times 3 = 18$$ cm2
  • Total Area: $$64 - 18 = 46$$ cm2
  • Perimeter: $$8 + 8 + 2 + 5 + 6 + 3 = 32$$ cm

Note: The provided OCR has handwritten calculations 'S=108' and 'P=28'. These do not match the visible dimensions.

Figure 6:

This figure can be divided into two rectangles. A larger rectangle with dimensions 20 cm by 10 cm, and a smaller rectangle with dimensions 10 cm by 5 cm.

  • Area of the first rectangle: $$20 \times 10 = 200$$ cm2
  • Area of the second rectangle: $$10 \times 5 = 50$$ cm2
  • Total Area: $$200 + 50 = 250$$ cm2
  • Perimeter: $$20 + 10 + 10 + 5 + 10 + 15 = 70$$ cm

Figure 7:

This figure can be divided into two rectangles. A larger rectangle with dimensions 12 cm by 6 cm and a smaller rectangle with dimensions 8 cm by 2 cm.

  • Area of the larger rectangle: $$12 \times 6 = 72$$ cm2
  • Area of the smaller rectangle: $$8 \times 2 = 16$$ cm2
  • Total Area: $$72 + 16 = 88$$ cm2
  • Perimeter: $$6 + 12 + 2 + 8 + 6 + 10 = 44$$ cm

Figure 8:

This is a large square with a smaller square removed from the center. The outer square has sides of 12 cm and the inner square has sides of 6 cm.

  • Area of the outer square: $$12 \times 12 = 144$$ cm2
  • Area of the inner square: $$6 \times 6 = 36$$ cm2
  • Total Area: $$144 - 36 = 108$$ cm2
  • Perimeter: $$12 + 12 + 12 + 12 = 48$$ cm

Figure 9:

This figure can be divided into two rectangles. A larger rectangle with dimensions 10 cm by 12 cm and a smaller rectangle with dimensions 8 cm by 4 cm.

  • Area of the first rectangle: $$10 \times 12 = 120$$ cm2
  • Area of the second rectangle: $$8 \times 4 = 32$$ cm2
  • Total Area: $$120 + 32 = 152$$ cm2
  • Perimeter: $$10 + 12 + 4 + 8 + 6 + 12 = 52$$ cm
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