Math topic中文

Shaded areas with circles and sectors

Find shaded areas in figures combining circles, sectors and polygons by cutting, filling, translating and using inclusion-exclusion.

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Arc sector segment

Practice questions

  1. 1A big circle and a small circle with centre O are drawn and each circle is divided into 4 quarter circles as shown. AOB…
  2. 2The diagram below shows 4 identical right-angled isosceles triangles with a quadrant within it. The quadrant has a radiu…
  3. 3Three concentric circles centered at OO have radii of 11, 22, and 33. Points BB and CC lie on the largest circle.…
  4. 4The figure below is made up of 2 identical big semi-circles and 3 identical small semi-circles. Find the perimeter of th…
  5. 5In the figure shown, US‾\overline{US} and UT‾\overline{UT} are line segments each of length 2, and m∠TUS=60∘m\angle TUS = 60^{\circ}…
  6. 6The circle shown below on the left has a radius of 1 unit. The region between the circle and the inscribed square is sha…
  7. 7The region shown below consists of 24 squares, each with side length 1 centimeter. What is the area, in square centimete…
  8. 8Squares of side length 1, 1, 2, 3, and 5 are arranged to form the rectangle shown below. A curve is drawn by inscribing…
  9. 9The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the…
  10. 10A roll of tape is 44 inches in diameter and is wrapped around a ring that is 22 inches in diameter. A cross section of…
  11. 11Sergei skated around an ice rink, gliding along different paths. The gray lines in the figures below show four of the pa…
  12. 12下图由大、小两个正方形组成，已知小正方形的边长为 6，大正方形的边长为 8，三角形 ABCABC 的面积是 ___.
  13. 13Lakshmi has 5 round coins of diameter 2 centimeters. She arranges the coins in 2 rows on a table top, as shown below, an…
  14. 14The figure below is made up of four squares of sides 10 cm, four quadrants and eight semicircles. Find the total area of…
  15. 15The figure below is made up of a rectangle, a circle and 2 identical semicircles. The diameters of the circle and the se…
  16. 16The figure below shows 2 identical semicircles and a rectangle. O and N are the centres of the semicircles. The length a…
  17. 17In the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller…
  18. 18The figure below shows a large white circle with a number of smaller white and shaded circles in its interior. What frac…