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Measures and solids · Ages 14–15

Segments and composite figures worksheet

Part of: Arc lengths & sectors

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Segments and composite figures worksheet

Measures and solids · Ages 14–15

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

Part A: Working out and filling in (2 marks each)

  1. 1.The window in the picture is a square of side 12 cm with a semicircle on top. Taking π as 3.14, what is the window's area, in cm²?

    Answer:

  2. 2.The sector in the picture has a radius of 4 cm and a right angle at the centre; the shaded part is a segment. The sector is π cm², the triangle cm², and the segment is the one less the other.

    Fill in each blank

    Answer:

  3. 3.The square in the picture has sides of 15 cm; the quarter circle has its centre at one corner and the side as its radius. Taking π as 3.14, what is the shaded area, in cm²?

    Answer:

  4. 4.The window in the picture is a square of side 10 cm with a semicircle on top. Taking π as 3.14, what is the window's area, in cm²?

    Answer:

  5. 5.The square in the picture has sides of 12 cm; the two quarter circles have their centres at opposite corners. Taking π as 3.14, what is the area of the shaded leaf, in cm²?

    Answer:

  6. 6.A semicircle has been cut out of the top side of the square in the picture, whose sides are 22 cm. Taking π as 3.14, what is the shaded part's perimeter, in cm?

    Answer:

  7. 7.The shaded part in the picture is a ring sector: angle 120°, outer radius 19 cm, inner radius 13 cm. What is its area, in terms of π?

    Answer:

  8. 8.The shaded part in the picture is a ring sector: angle 45°, outer radius 17 cm, inner radius 13 cm. What is its area, in terms of π?

    Answer:

  9. 9.A semicircle has been cut out of the top side of the square in the picture, whose sides are 30 cm. Taking π as 3.14, what is the shaded part's perimeter, in cm?

    Answer:

  10. 10.The square in the picture has sides of 2 cm; the two quarter circles have their centres at opposite corners. Taking π as 3.14, what is the area of the shaded leaf, in cm²?

    Answer:

  11. 11.The shaded ring sector in the picture has an angle of 45°, an outer radius of 13 cm and an inner one of 3 cm. Its perimeter is (π + ) cm.

    Fill in each blank

    Answer:

  12. 12.The sector in the picture has a radius of 14 cm and a right angle at the centre. Correct to 1 decimal place, what is the area of the shaded segment, in cm²?

    Answer:

Part B: Word problems (4 marks each)

  1. 13.A quarter-circle board of radius 10 cm is sawn along the straight line between its ends, leaving the segment in the picture. Taking π as 3.14, find the segment's area: put the steps in order.

    • A. Triangle = 10 × 10 ÷ 2 = 50
    • B. Sector = 14 × 3.14 × 102 = 78.5
    • C. Segment = 78.5 − 50 = 28.5

    Write the letters in the right order

    Working:

    Answer:

  2. 14.A car's wiper reaches 51 cm from its pivot, the rubber blade from 11 cm to 51 cm out, and it swings through 135°, wiping a ring sector. Its area is π cm² in terms of π, and cm² taking π as 3.14.

    Fill in each blank

    Working:

    Answer:

  3. 15.A window is a rectangle 40 cm wide and 90 cm high with a semicircle 40 cm across on top. Taking π as 3.14, what is its area of glass, in cm²?

    Working:

    Answer:

  4. 16.Each square tile has sides of 28 cm and the leaf in the picture painted on it (where two quarter circles overlap). Taking π as 3.14, one tile's leaf is cm²; 70 tiles' are cm².

    Fill in each blank

    Working:

    Answer:

  5. 17.Each square tile has sides of 12 cm and the leaf in the picture painted on it (where two quarter circles overlap). Taking π as 3.14, one tile's leaf is cm²; 30 tiles' are cm².

    Fill in each blank

    Working:

    Answer:

  6. 18.A quarter-circle board of radius 12 cm is sawn along the straight line between its ends, leaving the segment in the picture. Taking π as 3.14, find the segment's area: put the steps in order.

    • A. Triangle = 12 × 12 ÷ 2 = 72
    • B. Sector = 14 × 3.14 × 122 = 113.04
    • C. Segment = 113.04 − 72 = 41.04

    Write the letters in the right order

    Working:

    Answer:

Show the answers and working

Segments and composite figures worksheet: Answers and working

Part A: Working out and filling in

  1. 1. 200.52 cm²

    Square 144; the semicircle's radius is 6: 12 × 3.14 × 62 = 56.52; 200.52 cm² in all.

  2. 2. 4, 8

    Sector 90360 × π × 42 = 4π; triangle 4 × 4 ÷ 2 = 8; segment = (4π − 8) cm².

  3. 3. 48.375 cm²

    Shaded = square − quarter circle = 225 − 14 × 3.14 × 152 = 225 − 176.625 = 48.375 cm².

  4. 4. 139.25 cm²

    Square 100; the semicircle's radius is 5: 12 × 3.14 × 52 = 39.25; 139.25 cm² in all.

  5. 5. 82.08 cm²

    The leaf is two segments, each a quarter circle 113.04 − a triangle 72: 2 × (113.04 − 72) = 82.08 cm². Or two quarter circles − the square: 2 × 113.04 − 144.

  6. 6. 100.54 cm

    Three straight sides 3 × 22 = 66, plus the semicircle's arc 3.14 × 11 = 34.54 (the side cut away is no longer on the edge): 100.54 cm.

  7. 7. 64 π cm²

    Big sector − small sector = 120360 × π(192 − 132) = 64π cm².

  8. 8. 15 π cm²

    Big sector − small sector = 45360 × π(172 − 132) = 15π cm².

  9. 9. 137.1 cm

    Three straight sides 3 × 30 = 90, plus the semicircle's arc 3.14 × 15 = 47.1 (the side cut away is no longer on the edge): 137.1 cm.

  10. 10. 2.28 cm²

    The leaf is two segments, each a quarter circle 3.14 − a triangle 2: 2 × (3.14 − 2) = 2.28 cm². Or two quarter circles − the square: 2 × 3.14 − 4.

  11. 11. 4, 20

    Two arcs: 45360 × 2π × (13 + 3) = 4π; two straight sides of 13 − 3 each, 20 together.

  12. 12. 55.9 cm²

    The sector 14 × π × 142 less the triangle 98, rounded at the end: about 55.9 cm².

Part B: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

  1. 13. B → A → C

    Segment = sector − triangle = 78.5 − 50 = 28.5 cm².

  2. 14. 930, 2920.2

    135360 × π(512 − 112) = 930π; × 3.14 = 2920.2 cm².

  3. 15. 4228 cm²

    Rectangle 40 × 90 = 3600; the semicircle's radius is 20: 12 × 3.14 × 202 = 628; 4228 cm² in all.

  4. 16. 446.88, 31281.6

    Leaf = 2 × (14 × 3.14 × 282 − 282 ÷ 2) = 0.57 × 282 = 446.88; × 70 = 31281.6 cm².

  5. 17. 82.08, 2462.4

    Leaf = 2 × (14 × 3.14 × 122 − 122 ÷ 2) = 0.57 × 122 = 82.08; × 30 = 2462.4 cm².

  6. 18. B → A → C

    Segment = sector − triangle = 113.04 − 72 = 41.04 cm².

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