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Zorluk: OrtaPerimeter and Area of Plane Shapes

A circle of radius 7 cm7\text{ cm} is inscribed inside a square. What is the area of the region inside the square but outside the circle? (Take π=227\pi = \frac{22}{7})

  1. 42 cm242\text{ cm}^2Cevap
  2. B
    154 cm2154\text{ cm}^2
  3. C
    196 cm2196\text{ cm}^2
  4. D
    12 cm212\text{ cm}^2

Cevap

The area of the region inside the square but outside the circle is 42 cm242\text{ cm}^2.
Because the circle is inscribed inside the square, the diameter of the circle is equal to the side length of the square: s=2r=2(7)=14 cms = 2r = 2(7) = 14\text{ cm}. The area of the square is 142=196 cm214^2 = 196\text{ cm}^2. The area of the circle is πr2=227×72=154 cm2\pi r^2 = \frac{22}{7} \times 7^2 = 154\text{ cm}^2. Subtracting the area of the circle from the area of the square gives the region inside the square but outside the circle: 196−154=42 cm2196 - 154 = 42\text{ cm}^2.

Adım Adım Çözüm

1
Determine the side length of the square.
Side length s=2×7 cm=14 cms = 2 \times 7\text{ cm} = 14\text{ cm}.
An inscribed circle touches all four sides of the square, so its diameter equals the side length of the square.
2
Calculate the area of the square.
Area of square =s2=142=196 cm2= s^2 = 14^2 = 196\text{ cm}^2.
The area of a square with side length ss is given by s2s^2.
3
Calculate the area of the inscribed circle.
Area of circle =πr2=227×72=22×7=154 cm2= \pi r^2 = \frac{22}{7} \times 7^2 = 22 \times 7 = 154\text{ cm}^2.
The area of a circle with radius rr is given by πr2\pi r^2.
4
Subtract the circle's area from the square's area to find the area of the shaded outer region.
Area =196 cm2−154 cm2=42 cm2= 196\text{ cm}^2 - 154\text{ cm}^2 = 42\text{ cm}^2.
The remaining area consists of the four corner regions between the circle and the bounding square.

Anahtar Kavram

Area of composite plane figures (shaded area between inscribed shape and container)
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Konular

Perimeter and Area of Plane Shapes

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